<div class="xblock xblock-public_view xblock-public_view-vertical" data-block-type="vertical" data-runtime-version="1" data-usage-id="block-v1:MITx+18.05r_10+2022_Summer+type@vertical+block@class22-prep-a" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+18.05r_10+2022_Summer" data-has-score="False" data-init="VerticalStudentView" data-request-token="9030966adb8a11efb021029b57e3cc89">
<h2 class="hd hd-2 unit-title">Confidence intervals for normal data</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+18.05r_10+2022_Summer+type@html+block@class22-prep-a_hashpdf">
<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-block-type="html" data-runtime-version="1" data-usage-id="block-v1:MITx+18.05r_10+2022_Summer+type@html+block@class22-prep-a_hashpdf" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+18.05r_10+2022_Summer" data-has-score="False" data-init="XBlockToXModuleShim" data-request-token="9030966adb8a11efb021029b57e3cc89">
<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/v1/8b94e310c9c7d6c0da4c43974672bf26/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/pdf_mit18_05_s22_class22-prep-a.pdf">here</a></p><iframe src="/assets/courseware/v1/8b94e310c9c7d6c0da4c43974672bf26/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/pdf_mit18_05_s22_class22-prep-a.pdf" width="100%" height="1000px"> </iframe>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-block-type="vertical" data-runtime-version="1" data-usage-id="block-v1:MITx+18.05r_10+2022_Summer+type@vertical+block@class22-rq1-vertical" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+18.05r_10+2022_Summer" data-has-score="False" data-init="VerticalStudentView" data-request-token="9030966adb8a11efb021029b57e3cc89">
<h2 class="hd hd-2 unit-title">Class 22 reading questions: confidence intervals</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@c22-rq11">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-block-type="problem" data-runtime-version="1" data-usage-id="block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@c22-rq11" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+18.05r_10+2022_Summer" data-has-score="True" data-init="XBlockToXModuleShim" data-request-token="9030966adb8a11efb021029b57e3cc89">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_c22-rq11" class="problems-wrapper" role="group"
aria-labelledby="c22-rq11-problem-title"
data-problem-id="block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@c22-rq11" data-url="/courses/course-v1:MITx+18.05r_10+2022_Summer/xblock/block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@c22-rq11/handler/xmodule_handler"
data-problem-score="0.0"
data-problem-total-possible="2.0"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="c22-rq11-problem-title" aria-describedby="block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@c22-rq11-problem-progress" tabindex="-1">
Problem 1
</h3>
<div class="problem-progress" id="block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@c22-rq11-problem-progress"></div>
<div class="problem">
<div>
<p>
Be sure to give your answers to at least 3 significant digits. The answer boxes also accept Matlab style arithmetic expressions. </p>
<p><b class="bf">1.</b> Suppose you have [mathjaxinline]9[/mathjaxinline] data points drawn from [mathjaxinline]N(\mu ,1)[/mathjaxinline] with sample mean [mathjaxinline]\overline{x}= 3[/mathjaxinline]. What is the 95% confidence interval for the mean [mathjaxinline]\mu[/mathjaxinline]? (Use the approximation 2 instead of 1.96 for [mathjaxinline]z_{0.025}[/mathjaxinline].) </p>
<p>
Give the lower limit: <div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_c22-rq11_2_1" class=" capa_inputtype textline">
<div class="unanswered ">
<input type="text" name="input_c22-rq11_2_1" id="input_c22-rq11_2_1" aria-describedby="status_c22-rq11_2_1" value=""/>
<span class="trailing_text" id="trailing_text_c22-rq11_2_1"/>
<span class="status unanswered" id="status_c22-rq11_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_c22-rq11_2_1" class="answer"/>
</div>
</div></div> </p>
<p>
Give the upper limit: <div class="wrapper-problem-response" tabindex="-1" aria-label="Question 2" role="group"><div id="inputtype_c22-rq11_3_1" class=" capa_inputtype textline">
<div class="unanswered ">
<input type="text" name="input_c22-rq11_3_1" id="input_c22-rq11_3_1" aria-describedby="status_c22-rq11_3_1" value=""/>
<span class="trailing_text" id="trailing_text_c22-rq11_3_1"/>
<span class="status unanswered" id="status_c22-rq11_3_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_c22-rq11_3_1" class="answer"/>
</div>
</div></div> </p>
<p>
<div class="solution-span">
<span id="solution_c22-rq11_solution_1"/>
</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_c22-rq11" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_c22-rq11">
<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="c22-rq11-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="c22-rq11-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="c22-rq11-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="True">
<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@c22-rq12">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-block-type="problem" data-runtime-version="1" data-usage-id="block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@c22-rq12" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+18.05r_10+2022_Summer" data-has-score="True" data-init="XBlockToXModuleShim" data-request-token="9030966adb8a11efb021029b57e3cc89">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_c22-rq12" class="problems-wrapper" role="group"
aria-labelledby="c22-rq12-problem-title"
data-problem-id="block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@c22-rq12" data-url="/courses/course-v1:MITx+18.05r_10+2022_Summer/xblock/block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@c22-rq12/handler/xmodule_handler"
data-problem-score="0.0"
data-problem-total-possible="1.0"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="c22-rq12-problem-title" aria-describedby="block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@c22-rq12-problem-progress" tabindex="-1">
Problem 2
</h3>
<div class="problem-progress" id="block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@c22-rq12-problem-progress"></div>
<div class="problem">
<div>
<p><b class="bf">2.</b> Suppose you have [mathjaxinline]9[/mathjaxinline] data points drawn from [mathjaxinline]N(\mu ,\sigma ^2)[/mathjaxinline]. Suppose that [4.2, 6,8] is a 95% confidence interval for [mathjaxinline]\mu[/mathjaxinline]. </p>
<p>
What is the probability that [mathjaxinline]4.2 \le \mu \le 6.8[/mathjaxinline]? </p>
<p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_c22-rq12_2_1">
<fieldset aria-describedby="status_c22-rq12_2_1">
<div class="field">
<input type="radio" name="input_c22-rq12_2_1" id="input_c22-rq12_2_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="c22-rq12_2_1-choice_1-label" for="input_c22-rq12_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_c22-rq12_2_1">
<text> 0.95</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_c22-rq12_2_1" id="input_c22-rq12_2_1_choice_2" class="field-input input-radio" value="choice_2"/><label id="c22-rq12_2_1-choice_2-label" for="input_c22-rq12_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_c22-rq12_2_1">
<text> 0.05</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_c22-rq12_2_1" id="input_c22-rq12_2_1_choice_3" class="field-input input-radio" value="choice_3"/><label id="c22-rq12_2_1-choice_3-label" for="input_c22-rq12_2_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_c22-rq12_2_1">
<text> 0.95/3</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_c22-rq12_2_1" id="input_c22-rq12_2_1_choice_4" class="field-input input-radio" value="choice_4"/><label id="c22-rq12_2_1-choice_4-label" for="input_c22-rq12_2_1_choice_4" class="response-label field-label label-inline" aria-describedby="status_c22-rq12_2_1">
<text> Frequentists do not compute probabilities of hypotheses</text>
</label>
</div>
<span id="answer_c22-rq12_2_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_c22-rq12_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div>
</p>
<p>
<div class="solution-span">
<span id="solution_c22-rq12_solution_1"/>
</div></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_c22-rq12" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_c22-rq12">
<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="c22-rq12-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="c22-rq12-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="c22-rq12-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="True">
<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>
</div>