113 lines
3.1 KiB
Plaintext
113 lines
3.1 KiB
Plaintext
<section xml:id="sec-Confidence-Intervals" xmlns:xi="http://www.w3.org/2001/XInclude">
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<title>Confidence Intervals</title>
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<p>
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Text of section.
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</p>
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<exercises xml:id="exercises-Confidence-Intervals">
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<exercise>
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<statement>
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<p>
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Suppose we flip a coin 100 times and count 60 heads.
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Let <m>p</m> be the (unknown) probability that the coin comes up heads on a flip.
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Give an approximate 95% confidence interval for the value of <m>p</m>.
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</p>
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</statement>
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</exercise>
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<exercise>
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<introduction>
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<p>
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Suppose in a sample of 100 people, 12 are left-handed.
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</p>
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</introduction>
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<task>
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<statement>
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<p>
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Give a 95% confidence interval for the proportion <m>p</m> of left-handed people.
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</p>
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</statement>
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</task>
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<task>
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<statement>
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<p>
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Give a 90% confidence interval.
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</p>
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</statement>
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</task>
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</exercise>
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<exercise>
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<statement>
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<p>
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The weights of five mice are measured and recorded below.
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Give a 95% confidence interval for the sample mean weight of mice.
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(Pretend 5 measurements is large enough for the CLT to apply.)
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</p>
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<table>
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<title></title>
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<tabular>
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<row header="yes">
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<cell halign="center">mouse <m>i</m></cell>
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<cell halign="center">1</cell>
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<cell halign="center">2</cell>
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<cell halign="center">3</cell>
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<cell halign="center">4</cell>
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<cell halign="center">5</cell>
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</row>
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<row>
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<cell halign="center">weight <m>\widetilde{w}_i</m> (g)</cell>
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<cell halign="center">26</cell>
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<cell halign="center">32</cell>
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<cell halign="center">33</cell>
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<cell halign="center">20</cell>
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<cell halign="center">29</cell>
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</row>
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</tabular>
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</table>
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</statement>
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</exercise>
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<exercise>
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<statement>
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<p>
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The heights of five plants are measured and recorded below.
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Give a 95% confidence interval around the sample mean for the heights of the plants.
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(Pretend 5 measurements is large enough for the CLT to apply.)
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</p>
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<table>
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<title></title>
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<tabular>
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<row header="yes">
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<cell halign="center">plant <m>i</m></cell>
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<cell halign="center">1</cell>
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<cell halign="center">2</cell>
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<cell halign="center">3</cell>
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<cell halign="center">4</cell>
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<cell halign="center">5</cell>
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</row>
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<row>
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<cell halign="center">height <m>\widetilde{h}_i</m> (in)</cell>
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<cell halign="center">15</cell>
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<cell halign="center">14</cell>
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<cell halign="center">18</cell>
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<cell halign="center">21</cell>
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<cell halign="center">17</cell>
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</row>
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</tabular>
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</table>
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</statement>
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</exercise>
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</exercises>
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</section> |