# Chapter 1. Large-Sample Confidence Intervals for Comparing Proportions

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Stat Tutor
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1:02

### Question 1.1

FMjVyffpIymRLY58ZYMzGGlFLrWtq7Rjh39UM7qbOp1ugQCxC+ShNm8xLtE4zV3YpKatSy48kpxMKPfW+WFN8oMOhBTGbO1/rTTCxv0UOpIRIR0/SPSjN8Onsi5tRN7Nx6rFvgCEmkJPWJ+hCt/6i3m89IJyI8xzrYW4VYIvM5EgsLLXsW2c28NHfCzT7ZZeXYSSUWY+jn+LbEWMKt1sD+CP3RegSX2Ho+lg4jUrqt65U4RW6f0DbJWcAMpP/q4Ea6fhbYToQhew/afg98b96Blkmhlehr4PfovnwhEmUxEt7ecrpd4RzWxV+RghZfoFY1O01BYouV0JP/WpGLO0yyl2lNT4lRrWxPdSMg==
Incorrect. The name for $$\widehat{p}_{1}$$ - $$\widehat{p}_{2}$$ is the difference between two sample proportions. This is a statistic.
Correct. The name for $$\widehat{p}_{1}$$ - $$\widehat{p}_{2}$$ is the difference between two sample proportions. This is a statistic.
Incorrect. Try again.
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2:00

### Question 1.2

KPjjQ7LwnUN0/0sjWSMRnObBfgEYB8H267IBtcPa6lrxM/98+0PM/oJfFTKUhTa8Gdz5eUsl3PkeERS+H48eE/JCLRHPBfpYtQ5fkDfXYiCJB8ifYl1D2KKtu4vUFItGoD30VQj/xtlVDbR3yXRf0iuXXHNESAyhXHYKZX6volQPmDNduv306Hf8f1Cs9F+y14DWTEVDNe+wmIuLQDFVn/1jGt95STTJcE6eBX1vSswp9nTGvxWTv+ebIP3VBEnGPdM8nfA1k+m73bmI7o5/9jdewAfcm3R6r3Zv30fkjWJK58rw9vvC63W55xrphwCuiUCw2gcbw5mhqo13gQH+0LkKzkSY7aMOaloy0i5GoUhpqLPuCBFfOnCbqZnHLyQlzcaJCvmeE3bgm/t0vQL2QA==
Incorrect. The name for p1 - p2 is the difference between two population proportions.
Correct. The name for p1 - p2 is the difference between two population proportions.
Incorrect. Try again.
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2:32

### Question 1.3

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
Incorrect. The values for p1 and p2 are unknown as we are trying to estimate them and yet the formula requires values for them.
Correct. The values for p1 and p2 are unknown as we are trying to estimate them and yet the formula requires values for them.
Incorrect. Try again.
2

3:15

### Question 1.4

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Incorrect. $$n_{1}\widehat{p}_{1} \geq 5$$, $$n_{1}(1-\widehat{p}_{1}) \geq 5$$, $$n_{2}\widehat{p}_{2} \geq 5$$, and $$n_{2}(1-\widehat{p}_{2}) \geq 5$$ is the other necessary condition. These are actually the observed counts in all four cellsâ€”they all need to be five or bigger.
Correct. $$n_{1}\widehat{p}_{1} \geq 5$$, $$n_{1}(1-\widehat{p}_{1}) \geq 5$$, $$n_{2}\widehat{p}_{2} \geq 5$$, and $$n_{2}(1-\widehat{p}_{2}) \geq 5$$ is the other necessary condition. These are actually the observed counts in all four cellsâ€”they all need to be five or bigger.
Incorrect. Try again.
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4:28

### Question 1.5

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Incorrect. Matched pairs data should never be analyzed with this two-sample procedure for estimating p1 - p2 with a confidence interval.
Correct. Matched pairs data should never be analyzed with this two-sample procedure for estimating p1 - p2 with a confidence interval.
Incorrect. Try again.
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4:54

### Question 1.6

4nm2Rl2pE1eKRYL+NEu81Q9aGq18wEI27u0DaIORDDvdkPpwfDBqLVyozwwKogq1QjxNsi1TIlNRH//GOfj+elfLKsvkMtoKa0Kcwh5lYw484XGQfnSKO5oJmScKYCk5xlzqNw5BGoSpQ/u+J4PgIHA51BU/1pRQMLfD8/6oGQkU1qsepSdyctl+n1Ds1I/WaXUEnnoRaW7rwt1Y4Ybzq1j4vsiiY4ud6iGR3onEfVDqDRlJotkXZROXwtMsr8j5MRSQERbGWWtiOYZI3PSaKpiPvjAzym1q6dbqL3sQH2eOtCXv
Correct. The name for $$z^{*} \sqrt{ \frac{\widehat{p}_{1}(1-\widehat{p}_{1})}{ n_{1} } + \frac{\widehat{p}_{2}(1-\widehat{p}_{2})}{ n_{2} }}$$ is margin of error.
Incorrect. Try again.
2
Incorrect. The name for$$z^{*} \sqrt{ \frac{\widehat{p}_{1}(1-\widehat{p}_{1})}{ n_{1} } + \frac{\widehat{p}_{2}(1-\widehat{p}_{2})}{ n_{2} }}$$ is margin of error.

5:46

### Question 1.7

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Incorrect. Data were collected using a randomized experiment with subjects randomly allocated to treatments.
Correct. Data were collected using a randomized experiment with subjects randomly allocated to treatments.
Incorrect. Try again.
2

### Question 1.8

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Incorrect. The cell counts are 104, 10933, 189 and 10845; all are bigger than 5, so the sample sizes are large enough for approximate Normality.
Correct. The cell counts are 104, 10933, 189 and 10845; all are bigger than 5, so the sample sizes are large enough for approximate Normality.
Incorrect. Try again.
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7:43

### Question 1.9

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Incorrect. The value of z* for 95% confidence is 1.960.
Correct. The value of z* for 95% confidence is 1.960.
Incorrect. Try again.
2

8:47

### Question 1.10

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Incorrect. The name for the value 0.003 is margin of error.
Correct. The name for the value 0.003 is margin of error.
Incorrect. Try again.
2

9:01

### Question 1.11

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
Incorrect. This confidence interval estimates p1 - p2 or the difference between the two treatment proportions. p1= proportion of doctors having a heart attack while taking aspiring and p2 = the proportion of doctors having a heart attack while taking a placebo. Thus, the interval tells us that the difference between the proportion of doctors taking aspirin having a heart attack and the proportion of doctors taking a placbo having a heart attack is somewhere -0.011 and -0.005 with 95% confidence.
Correct. This confidence interval estimates p1 - p2 or the difference between the two treatment proportions. p1= proportion of doctors having a heart attack while taking aspiring and p2 = the proportion of doctors having a heart attack while taking a placebo. Thus, the interval tells us that the difference between the proportion of doctors taking aspirin having a heart attack and the proportion of doctors taking a placbo having a heart attack is somewhere -0.011 and -0.005 with 95% confidence.
Incorrect. Try again.
2

9:48

### Question 1.12

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Incorrect. The answer to this question is subject to debate. Depending on how you look at it both answers could be correct. Some say that doctors don't take very good care of their physical health. Others might argue that doctors are more aware of potential outcomes. What is your opinion?
Correct. The answer to this question is subject to debate. Depending on how you look at it both answers could be correct. Some say that doctors don't take very good care of their physical health. Others might argue that doctors are more aware of potential outcomes. What is your opinion?
Incorrect. Try again.
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