<div class="xblock xblock-public_view xblock-public_view-vertical" data-course-id="course-v1:MITx+18.05r_10+2022_Summer" data-has-score="False" data-runtime-version="1" data-block-type="vertical" data-request-token="1c22aedab23f11ef92510e328d43dba3" data-usage-id="block-v1:MITx+18.05r_10+2022_Summer+type@vertical+block@ps9" data-graded="False" data-init="VerticalStudentView" data-runtime-class="LmsRuntime">
<h2 class="hd hd-2 unit-title">Problem set 9</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+18.05r_10+2022_Summer+type@html+block@ps9_hashpdf">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-course-id="course-v1:MITx+18.05r_10+2022_Summer" data-has-score="False" data-runtime-version="1" data-block-type="html" data-request-token="1c22aedab23f11ef92510e328d43dba3" data-usage-id="block-v1:MITx+18.05r_10+2022_Summer+type@html+block@ps9_hashpdf" data-graded="False" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "HTMLModule"}
</script>
<p>You can download this pdf file from <a href="/assets/courseware/v1/458d6c250bc397f7ddb5f37ecde7b479/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/pdf_mit18_05_s22_ps9.pdf">here</a></p><iframe src="/assets/courseware/v1/458d6c250bc397f7ddb5f37ecde7b479/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/pdf_mit18_05_s22_ps9.pdf" width="100%" height="1000px"> </iframe>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-course-id="course-v1:MITx+18.05r_10+2022_Summer" data-has-score="False" data-runtime-version="1" data-block-type="vertical" data-request-token="1c22aedab23f11ef92510e328d43dba3" data-usage-id="block-v1:MITx+18.05r_10+2022_Summer+type@vertical+block@ps9-checkvertical" data-graded="False" data-init="VerticalStudentView" data-runtime-class="LmsRuntime">
<h2 class="hd hd-2 unit-title">Pset 9 problem checker</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@ps9-1-check">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-course-id="course-v1:MITx+18.05r_10+2022_Summer" data-has-score="True" data-runtime-version="1" data-block-type="problem" data-request-token="1c22aedab23f11ef92510e328d43dba3" data-usage-id="block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@ps9-1-check" data-graded="False" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_ps9-1-check" class="problems-wrapper" role="group"
aria-labelledby="ps9-1-check-problem-title"
data-problem-id="block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@ps9-1-check" data-url="/courses/course-v1:MITx+18.05r_10+2022_Summer/xblock/block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@ps9-1-check/handler/xmodule_handler"
data-problem-score="0"
data-problem-total-possible="0"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="ps9-1-check-problem-title" aria-describedby="block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@ps9-1-check-problem-progress" tabindex="-1">
Problem 1
</h3>
<div class="problem-progress" id="block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@ps9-1-check-problem-progress"></div>
<div class="problem">
<div>
<p>
To check your answers put them in the appropriate box and click the &#8216;Check' button. The checker can do arithmetic. So, 3^2, [mathjaxinline]5/3[/mathjaxinline] and [mathjaxinline]3*4[/mathjaxinline] are okay. </p>
<p>
Unless otherwise stated the checker expects numerical answers to 3 significant digits. </p>
<p>
For formulas you can use R notation. Remember to use a * for multiplication, i.e. [mathjaxinline]3*x[/mathjaxinline] <b class="bf">NOT </b> [mathjaxinline]3x[/mathjaxinline]. </p>
<p>
The checker knows many of the standard functions, e.g. use exp(x) and ln(x) for the exponential and natural log functions. </p>
<p>
The formula checker expects a specific letter for the variables, so be sure to use the ones specified. </p>
<p><b class="bf">1(a)</b> Give the [mathjaxinline]p[/mathjaxinline]-value of the test for this data (to at least 2 significant digits) <div class="inline" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_ps9-1-check_2_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
<div class="script_placeholder" data-src="/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/MJxPrep.js"/>
<div class="unanswered inline">
<input type="text" name="input_ps9-1-check_2_1" id="input_ps9-1-check_2_1" aria-describedby="status_ps9-1-check_2_1" value="" class="math" size="50"/>
<span class="trailing_text" id="trailing_text_ps9-1-check_2_1"/>
<span class="status unanswered" id="status_ps9-1-check_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_ps9-1-check_2_1" class="answer"/>
<div id="display_ps9-1-check_2_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ps9-1-check_2_1_dynamath" name="input_ps9-1-check_2_1_dynamath"/>
</div>
</div></div> </p>
<p><b class="bf">1(b)</b> Give the [mathjaxinline]p[/mathjaxinline]-value of the test for this data (to at least 2 significant digits) <div class="inline" tabindex="-1" aria-label="Question 2" role="group"><div id="inputtype_ps9-1-check_3_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
<div class="script_placeholder" data-src="/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/MJxPrep.js"/>
<div class="unanswered inline">
<input type="text" name="input_ps9-1-check_3_1" id="input_ps9-1-check_3_1" aria-describedby="status_ps9-1-check_3_1" value="" class="math" size="50"/>
<span class="trailing_text" id="trailing_text_ps9-1-check_3_1"/>
<span class="status unanswered" id="status_ps9-1-check_3_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_ps9-1-check_3_1" class="answer"/>
<div id="display_ps9-1-check_3_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ps9-1-check_3_1_dynamath" name="input_ps9-1-check_3_1_dynamath"/>
</div>
</div></div> </p>
</div>
<div class="action">
<input type="hidden" name="problem_id" value="Problem 1" />
<div class="submit-attempt-container">
<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_ps9-1-check" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_ps9-1-check">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
</div>
</div>
<div class="problem-action-buttons-wrapper">
<span class="problem-action-button-wrapper">
<button type="button" class="save problem-action-btn btn-default btn-small" data-value="Save">
<span class="icon fa fa-floppy-o" aria-hidden="true"></span>
<span aria-hidden="true">Save</span>
<span class="sr">Save your answer</span>
</button>
</span>
</div>
</div>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="ps9-1-check-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="ps9-1-check-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="ps9-1-check-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="False">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
<div class="vert vert-1" data-id="block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@ps9-2-check">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-course-id="course-v1:MITx+18.05r_10+2022_Summer" data-has-score="True" data-runtime-version="1" data-block-type="problem" data-request-token="1c22aedab23f11ef92510e328d43dba3" data-usage-id="block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@ps9-2-check" data-graded="False" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_ps9-2-check" class="problems-wrapper" role="group"
aria-labelledby="ps9-2-check-problem-title"
data-problem-id="block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@ps9-2-check" data-url="/courses/course-v1:MITx+18.05r_10+2022_Summer/xblock/block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@ps9-2-check/handler/xmodule_handler"
data-problem-score="0"
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<h3 class="hd hd-3 problem-header" id="ps9-2-check-problem-title" aria-describedby="block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@ps9-2-check-problem-progress" tabindex="-1">
Problem 2
</h3>
<div class="problem-progress" id="block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@ps9-2-check-problem-progress"></div>
<div class="problem">
<div>
<p>
<b class="bf">2(a)</b>
<b class="bf">Hint: the rejection region is one-sided.</b>
</p>
<p>
Give all the values in the rejection region (as a comma separated list) <div class="inline" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_ps9-2-check_2_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
<div class="script_placeholder" data-src="/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/MJxPrep.js"/>
<div class="unanswered inline">
<input type="text" name="input_ps9-2-check_2_1" id="input_ps9-2-check_2_1" aria-describedby="status_ps9-2-check_2_1" value="" class="math" size="50"/>
<span class="trailing_text" id="trailing_text_ps9-2-check_2_1"/>
<span class="status unanswered" id="status_ps9-2-check_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_ps9-2-check_2_1" class="answer"/>
<div id="display_ps9-2-check_2_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ps9-2-check_2_1_dynamath" name="input_ps9-2-check_2_1_dynamath"/>
</div>
</div></div> </p>
<p>
Give the [mathjaxinline]p[/mathjaxinline]-value (to at least 2 significant digits) <div class="inline" tabindex="-1" aria-label="Question 2" role="group"><div id="inputtype_ps9-2-check_3_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
<div class="script_placeholder" data-src="/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/MJxPrep.js"/>
<div class="unanswered inline">
<input type="text" name="input_ps9-2-check_3_1" id="input_ps9-2-check_3_1" aria-describedby="status_ps9-2-check_3_1" value="" class="math" size="50"/>
<span class="trailing_text" id="trailing_text_ps9-2-check_3_1"/>
<span class="status unanswered" id="status_ps9-2-check_3_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_ps9-2-check_3_1" class="answer"/>
<div id="display_ps9-2-check_3_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ps9-2-check_3_1_dynamath" name="input_ps9-2-check_3_1_dynamath"/>
</div>
</div></div> </p>
<p>
<b class="bf">(2b)</b>
<b class="bf">Hint: the rejection region is one-sided.</b>
</p>
<p>
Give smallest value in the rejection region <div class="inline" tabindex="-1" aria-label="Question 3" role="group"><div id="inputtype_ps9-2-check_4_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
<div class="script_placeholder" data-src="/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/MJxPrep.js"/>
<div class="unanswered inline">
<input type="text" name="input_ps9-2-check_4_1" id="input_ps9-2-check_4_1" aria-describedby="status_ps9-2-check_4_1" value="" class="math" size="50"/>
<span class="trailing_text" id="trailing_text_ps9-2-check_4_1"/>
<span class="status unanswered" id="status_ps9-2-check_4_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_ps9-2-check_4_1" class="answer"/>
<div id="display_ps9-2-check_4_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ps9-2-check_4_1_dynamath" name="input_ps9-2-check_4_1_dynamath"/>
</div>
</div></div> </p>
<p>
Give the [mathjaxinline]p[/mathjaxinline]-value (to 2 significant digits) <div class="inline" tabindex="-1" aria-label="Question 4" role="group"><div id="inputtype_ps9-2-check_5_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
<div class="script_placeholder" data-src="/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/MJxPrep.js"/>
<div class="unanswered inline">
<input type="text" name="input_ps9-2-check_5_1" id="input_ps9-2-check_5_1" aria-describedby="status_ps9-2-check_5_1" value="" class="math" size="50"/>
<span class="trailing_text" id="trailing_text_ps9-2-check_5_1"/>
<span class="status unanswered" id="status_ps9-2-check_5_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_ps9-2-check_5_1" class="answer"/>
<div id="display_ps9-2-check_5_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ps9-2-check_5_1_dynamath" name="input_ps9-2-check_5_1_dynamath"/>
</div>
</div></div> </p>
<p>
<b class="bf">(2c)</b>
<em>No answer checker given.</em>
</p>
<p>
<b class="bf">(2d)</b>
<em>No answer checker given.</em>
</p>
<p>
<b class="bf">(2e)</b>
<em>No answer checker given.</em>
</p>
</div>
<div class="action">
<input type="hidden" name="problem_id" value="Problem 2" />
<div class="submit-attempt-container">
<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_ps9-2-check" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_ps9-2-check">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
</div>
</div>
<div class="problem-action-buttons-wrapper">
<span class="problem-action-button-wrapper">
<button type="button" class="save problem-action-btn btn-default btn-small" data-value="Save">
<span class="icon fa fa-floppy-o" aria-hidden="true"></span>
<span aria-hidden="true">Save</span>
<span class="sr">Save your answer</span>
</button>
</span>
</div>
</div>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="ps9-2-check-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="ps9-2-check-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="ps9-2-check-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="False">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
<div class="vert vert-2" data-id="block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@ps9-3-check">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-course-id="course-v1:MITx+18.05r_10+2022_Summer" data-has-score="True" data-runtime-version="1" data-block-type="problem" data-request-token="1c22aedab23f11ef92510e328d43dba3" data-usage-id="block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@ps9-3-check" data-graded="False" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_ps9-3-check" class="problems-wrapper" role="group"
aria-labelledby="ps9-3-check-problem-title"
data-problem-id="block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@ps9-3-check" data-url="/courses/course-v1:MITx+18.05r_10+2022_Summer/xblock/block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@ps9-3-check/handler/xmodule_handler"
data-problem-score="0"
data-problem-total-possible="0"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="ps9-3-check-problem-title" aria-describedby="block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@ps9-3-check-problem-progress" tabindex="-1">
Problem 3
</h3>
<div class="problem-progress" id="block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@ps9-3-check-problem-progress"></div>
<div class="problem">
<div>
<p><b class="bf">3.</b> Give value of the [mathjaxinline]X^2[/mathjaxinline] test statistic (to 3 significant digits) <div class="inline" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_ps9-3-check_2_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
<div class="script_placeholder" data-src="/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/MJxPrep.js"/>
<div class="unanswered inline">
<input type="text" name="input_ps9-3-check_2_1" id="input_ps9-3-check_2_1" aria-describedby="status_ps9-3-check_2_1" value="" class="math" size="50"/>
<span class="trailing_text" id="trailing_text_ps9-3-check_2_1"/>
<span class="status unanswered" id="status_ps9-3-check_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_ps9-3-check_2_1" class="answer"/>
<div id="display_ps9-3-check_2_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ps9-3-check_2_1_dynamath" name="input_ps9-3-check_2_1_dynamath"/>
</div>
</div></div> </p>
<p>
Give the [mathjaxinline]p[/mathjaxinline]-value (to 2 significant digits) <div class="inline" tabindex="-1" aria-label="Question 2" role="group"><div id="inputtype_ps9-3-check_3_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
<div class="script_placeholder" data-src="/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/MJxPrep.js"/>
<div class="unanswered inline">
<input type="text" name="input_ps9-3-check_3_1" id="input_ps9-3-check_3_1" aria-describedby="status_ps9-3-check_3_1" value="" class="math" size="50"/>
<span class="trailing_text" id="trailing_text_ps9-3-check_3_1"/>
<span class="status unanswered" id="status_ps9-3-check_3_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_ps9-3-check_3_1" class="answer"/>
<div id="display_ps9-3-check_3_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ps9-3-check_3_1_dynamath" name="input_ps9-3-check_3_1_dynamath"/>
</div>
</div></div> </p>
</div>
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aria-labelledby="ps9-4-check-problem-title"
data-problem-id="block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@ps9-4-check" data-url="/courses/course-v1:MITx+18.05r_10+2022_Summer/xblock/block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@ps9-4-check/handler/xmodule_handler"
data-problem-score="0"
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<h3 class="hd hd-3 problem-header" id="ps9-4-check-problem-title" aria-describedby="block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@ps9-4-check-problem-progress" tabindex="-1">
Problem 4
</h3>
<div class="problem-progress" id="block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@ps9-4-check-problem-progress"></div>
<div class="problem">
<div>
<p><b class="bf">4.</b> (You only need to use one of the [mathjaxinline]G[/mathjaxinline] or [mathjaxinline]X^2[/mathjaxinline] statistics.) </p>
<p>
Give the [mathjaxinline]G[/mathjaxinline] statistic (3 significant digits) <div class="inline" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_ps9-4-check_2_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
<div class="script_placeholder" data-src="/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/MJxPrep.js"/>
<div class="unanswered inline">
<input type="text" name="input_ps9-4-check_2_1" id="input_ps9-4-check_2_1" aria-describedby="status_ps9-4-check_2_1" value="" class="math" size="50"/>
<span class="trailing_text" id="trailing_text_ps9-4-check_2_1"/>
<span class="status unanswered" id="status_ps9-4-check_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_ps9-4-check_2_1" class="answer"/>
<div id="display_ps9-4-check_2_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ps9-4-check_2_1_dynamath" name="input_ps9-4-check_2_1_dynamath"/>
</div>
</div></div> </p>
<p>
Give the [mathjaxinline]p[/mathjaxinline]-value corresponding to [mathjaxinline]G[/mathjaxinline] (Just give this to 4 decimal points.) <div class="inline" tabindex="-1" aria-label="Question 2" role="group"><div id="inputtype_ps9-4-check_3_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
<div class="script_placeholder" data-src="/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/MJxPrep.js"/>
<div class="unanswered inline">
<input type="text" name="input_ps9-4-check_3_1" id="input_ps9-4-check_3_1" aria-describedby="status_ps9-4-check_3_1" value="" class="math" size="50"/>
<span class="trailing_text" id="trailing_text_ps9-4-check_3_1"/>
<span class="status unanswered" id="status_ps9-4-check_3_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_ps9-4-check_3_1" class="answer"/>
<div id="display_ps9-4-check_3_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ps9-4-check_3_1_dynamath" name="input_ps9-4-check_3_1_dynamath"/>
</div>
</div></div> </p>
<p>
Give value of the [mathjaxinline]X^2[/mathjaxinline] test statistic (3 signifcant digits) <div class="inline" tabindex="-1" aria-label="Question 3" role="group"><div id="inputtype_ps9-4-check_4_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
<div class="script_placeholder" data-src="/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/MJxPrep.js"/>
<div class="unanswered inline">
<input type="text" name="input_ps9-4-check_4_1" id="input_ps9-4-check_4_1" aria-describedby="status_ps9-4-check_4_1" value="" class="math" size="50"/>
<span class="trailing_text" id="trailing_text_ps9-4-check_4_1"/>
<span class="status unanswered" id="status_ps9-4-check_4_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_ps9-4-check_4_1" class="answer"/>
<div id="display_ps9-4-check_4_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ps9-4-check_4_1_dynamath" name="input_ps9-4-check_4_1_dynamath"/>
</div>
</div></div> </p>
<p>
Give the [mathjaxinline]p[/mathjaxinline]-value corresponding to [mathjaxinline]X^2[/mathjaxinline] (Just give this to 4 decimal points) <div class="inline" tabindex="-1" aria-label="Question 4" role="group"><div id="inputtype_ps9-4-check_5_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
<div class="script_placeholder" data-src="/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/MJxPrep.js"/>
<div class="unanswered inline">
<input type="text" name="input_ps9-4-check_5_1" id="input_ps9-4-check_5_1" aria-describedby="status_ps9-4-check_5_1" value="" class="math" size="50"/>
<span class="trailing_text" id="trailing_text_ps9-4-check_5_1"/>
<span class="status unanswered" id="status_ps9-4-check_5_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_ps9-4-check_5_1" class="answer"/>
<div id="display_ps9-4-check_5_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ps9-4-check_5_1_dynamath" name="input_ps9-4-check_5_1_dynamath"/>
</div>
</div></div> </p>
</div>
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<input type="hidden" name="problem_id" value="Problem 4" />
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data-problem-id="block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@ps9-5-check" data-url="/courses/course-v1:MITx+18.05r_10+2022_Summer/xblock/block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@ps9-5-check/handler/xmodule_handler"
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Problem 5
</h3>
<div class="problem-progress" id="block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@ps9-5-check-problem-progress"></div>
<div class="problem">
<div>
<p><b class="bf">5.</b> The answers here to both (a) and (b) should be the same: </p>
<p>
Give the [mathjaxinline]F[/mathjaxinline]-statistic (2 significant digits) <div class="inline" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_ps9-5-check_2_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
<div class="script_placeholder" data-src="/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/MJxPrep.js"/>
<div class="unanswered inline">
<input type="text" name="input_ps9-5-check_2_1" id="input_ps9-5-check_2_1" aria-describedby="status_ps9-5-check_2_1" value="" class="math" size="50"/>
<span class="trailing_text" id="trailing_text_ps9-5-check_2_1"/>
<span class="status unanswered" id="status_ps9-5-check_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_ps9-5-check_2_1" class="answer"/>
<div id="display_ps9-5-check_2_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ps9-5-check_2_1_dynamath" name="input_ps9-5-check_2_1_dynamath"/>
</div>
</div></div> </p>
<p>
Give the [mathjaxinline]p[/mathjaxinline]-value (2 significant digits) <div class="inline" tabindex="-1" aria-label="Question 2" role="group"><div id="inputtype_ps9-5-check_3_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
<div class="script_placeholder" data-src="/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/MJxPrep.js"/>
<div class="unanswered inline">
<input type="text" name="input_ps9-5-check_3_1" id="input_ps9-5-check_3_1" aria-describedby="status_ps9-5-check_3_1" value="" class="math" size="50"/>
<span class="trailing_text" id="trailing_text_ps9-5-check_3_1"/>
<span class="status unanswered" id="status_ps9-5-check_3_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_ps9-5-check_3_1" class="answer"/>
<div id="display_ps9-5-check_3_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ps9-5-check_3_1_dynamath" name="input_ps9-5-check_3_1_dynamath"/>
</div>
</div></div> </p>
</div>
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<input type="hidden" name="problem_id" value="Problem 5" />
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<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_ps9-5-check" >
<span class="submit-label">Submit</span>
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<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
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<span class="sr">Loading…</span>
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<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-course-id="course-v1:MITx+18.05r_10+2022_Summer" data-has-score="True" data-runtime-version="1" data-block-type="problem" data-request-token="1c22aedab23f11ef92510e328d43dba3" data-usage-id="block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@ps9-6-check" data-graded="False" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime">
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{"xmodule-type": "Problem"}
</script>
<div id="problem_ps9-6-check" class="problems-wrapper" role="group"
aria-labelledby="ps9-6-check-problem-title"
data-problem-id="block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@ps9-6-check" data-url="/courses/course-v1:MITx+18.05r_10+2022_Summer/xblock/block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@ps9-6-check/handler/xmodule_handler"
data-problem-score="0"
data-problem-total-possible="0"
data-attempts-used="0"
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<h3 class="hd hd-3 problem-header" id="ps9-6-check-problem-title" aria-describedby="block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@ps9-6-check-problem-progress" tabindex="-1">
Problem 6
</h3>
<div class="problem-progress" id="block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@ps9-6-check-problem-progress"></div>
<div class="problem">
<div>
<p><b class="bf">6.</b> To check this problem you should not round intermediate values. For example if R gives a [mathjaxinline]F[/mathjaxinline]-statistic of 2.0000123 then do not round to 2 and use that in computing the [mathjaxinline]p[/mathjaxinline]-value. Instead, capture the statisic in a named variable and use the variable when computing the [mathjaxinline]p[/mathjaxinline]-value. </p>
<p><b class="bf">(6a)</b> Give the [mathjaxinline]F[/mathjaxinline]-statistic (3 significant digits) <div class="inline" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_ps9-6-check_2_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
<div class="script_placeholder" data-src="/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/MJxPrep.js"/>
<div class="unanswered inline">
<input type="text" name="input_ps9-6-check_2_1" id="input_ps9-6-check_2_1" aria-describedby="status_ps9-6-check_2_1" value="" class="math" size="50"/>
<span class="trailing_text" id="trailing_text_ps9-6-check_2_1"/>
<span class="status unanswered" id="status_ps9-6-check_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_ps9-6-check_2_1" class="answer"/>
<div id="display_ps9-6-check_2_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ps9-6-check_2_1_dynamath" name="input_ps9-6-check_2_1_dynamath"/>
</div>
</div></div> </p>
<p>
Give the [mathjaxinline]p[/mathjaxinline]-value (2 significant digits) <div class="inline" tabindex="-1" aria-label="Question 2" role="group"><div id="inputtype_ps9-6-check_3_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
<div class="script_placeholder" data-src="/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/MJxPrep.js"/>
<div class="unanswered inline">
<input type="text" name="input_ps9-6-check_3_1" id="input_ps9-6-check_3_1" aria-describedby="status_ps9-6-check_3_1" value="" class="math" size="50"/>
<span class="trailing_text" id="trailing_text_ps9-6-check_3_1"/>
<span class="status unanswered" id="status_ps9-6-check_3_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_ps9-6-check_3_1" class="answer"/>
<div id="display_ps9-6-check_3_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ps9-6-check_3_1_dynamath" name="input_ps9-6-check_3_1_dynamath"/>
</div>
</div></div> </p>
<p><b class="bf">(6b)</b> Comparing 10-day growth vs. clean shaven: Give the [mathjaxinline]t[/mathjaxinline]-statistic (3 significant digits) <div class="inline" tabindex="-1" aria-label="Question 3" role="group"><div id="inputtype_ps9-6-check_4_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
<div class="script_placeholder" data-src="/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/MJxPrep.js"/>
<div class="unanswered inline">
<input type="text" name="input_ps9-6-check_4_1" id="input_ps9-6-check_4_1" aria-describedby="status_ps9-6-check_4_1" value="" class="math" size="50"/>
<span class="trailing_text" id="trailing_text_ps9-6-check_4_1"/>
<span class="status unanswered" id="status_ps9-6-check_4_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_ps9-6-check_4_1" class="answer"/>
<div id="display_ps9-6-check_4_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ps9-6-check_4_1_dynamath" name="input_ps9-6-check_4_1_dynamath"/>
</div>
</div></div> </p>
<p>
Give the one-sided [mathjaxinline]p[/mathjaxinline]-value (2 significant digits) <div class="inline" tabindex="-1" aria-label="Question 4" role="group"><div id="inputtype_ps9-6-check_5_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
<div class="script_placeholder" data-src="/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/MJxPrep.js"/>
<div class="unanswered inline">
<input type="text" name="input_ps9-6-check_5_1" id="input_ps9-6-check_5_1" aria-describedby="status_ps9-6-check_5_1" value="" class="math" size="50"/>
<span class="trailing_text" id="trailing_text_ps9-6-check_5_1"/>
<span class="status unanswered" id="status_ps9-6-check_5_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_ps9-6-check_5_1" class="answer"/>
<div id="display_ps9-6-check_5_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ps9-6-check_5_1_dynamath" name="input_ps9-6-check_5_1_dynamath"/>
</div>
</div></div> </p>
<p>
Comparing 10-day growth vs. 5-day growth: Give the [mathjaxinline]t[/mathjaxinline]-statistic (3 significant digits) <div class="inline" tabindex="-1" aria-label="Question 5" role="group"><div id="inputtype_ps9-6-check_6_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
<div class="script_placeholder" data-src="/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/MJxPrep.js"/>
<div class="unanswered inline">
<input type="text" name="input_ps9-6-check_6_1" id="input_ps9-6-check_6_1" aria-describedby="status_ps9-6-check_6_1" value="" class="math" size="50"/>
<span class="trailing_text" id="trailing_text_ps9-6-check_6_1"/>
<span class="status unanswered" id="status_ps9-6-check_6_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_ps9-6-check_6_1" class="answer"/>
<div id="display_ps9-6-check_6_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ps9-6-check_6_1_dynamath" name="input_ps9-6-check_6_1_dynamath"/>
</div>
</div></div> </p>
<p>
Give the one-sided [mathjaxinline]p[/mathjaxinline]-value (2 significant digits) <div class="inline" tabindex="-1" aria-label="Question 6" role="group"><div id="inputtype_ps9-6-check_7_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
<div class="script_placeholder" data-src="/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/MJxPrep.js"/>
<div class="unanswered inline">
<input type="text" name="input_ps9-6-check_7_1" id="input_ps9-6-check_7_1" aria-describedby="status_ps9-6-check_7_1" value="" class="math" size="50"/>
<span class="trailing_text" id="trailing_text_ps9-6-check_7_1"/>
<span class="status unanswered" id="status_ps9-6-check_7_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_ps9-6-check_7_1" class="answer"/>
<div id="display_ps9-6-check_7_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ps9-6-check_7_1_dynamath" name="input_ps9-6-check_7_1_dynamath"/>
</div>
</div></div> </p>
<p>
Comparing 10-day growth vs. full beard: Give the [mathjaxinline]t[/mathjaxinline]-statistic (3 significant digits) <div class="inline" tabindex="-1" aria-label="Question 7" role="group"><div id="inputtype_ps9-6-check_8_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
<div class="script_placeholder" data-src="/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/MJxPrep.js"/>
<div class="unanswered inline">
<input type="text" name="input_ps9-6-check_8_1" id="input_ps9-6-check_8_1" aria-describedby="status_ps9-6-check_8_1" value="" class="math" size="50"/>
<span class="trailing_text" id="trailing_text_ps9-6-check_8_1"/>
<span class="status unanswered" id="status_ps9-6-check_8_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_ps9-6-check_8_1" class="answer"/>
<div id="display_ps9-6-check_8_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ps9-6-check_8_1_dynamath" name="input_ps9-6-check_8_1_dynamath"/>
</div>
</div></div> </p>
<p>
Give the one-sided [mathjaxinline]p[/mathjaxinline]-value (2 significant digits) <div class="inline" tabindex="-1" aria-label="Question 8" role="group"><div id="inputtype_ps9-6-check_9_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
<div class="script_placeholder" data-src="/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/MJxPrep.js"/>
<div class="unanswered inline">
<input type="text" name="input_ps9-6-check_9_1" id="input_ps9-6-check_9_1" aria-describedby="status_ps9-6-check_9_1" value="" class="math" size="50"/>
<span class="trailing_text" id="trailing_text_ps9-6-check_9_1"/>
<span class="status unanswered" id="status_ps9-6-check_9_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_ps9-6-check_9_1" class="answer"/>
<div id="display_ps9-6-check_9_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ps9-6-check_9_1_dynamath" name="input_ps9-6-check_9_1_dynamath"/>
</div>
</div></div> </p>
</div>
<div class="action">
<input type="hidden" name="problem_id" value="Problem 6" />
<div class="submit-attempt-container">
<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_ps9-6-check" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_ps9-6-check">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
</div>
</div>
<div class="problem-action-buttons-wrapper">
<span class="problem-action-button-wrapper">
<button type="button" class="save problem-action-btn btn-default btn-small" data-value="Save">
<span class="icon fa fa-floppy-o" aria-hidden="true"></span>
<span aria-hidden="true">Save</span>
<span class="sr">Save your answer</span>
</button>
</span>
</div>
</div>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="ps9-6-check-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="ps9-6-check-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="ps9-6-check-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
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"
data-graded="False">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
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