# Chapter 1. Significance Tests for Comparing Proportions

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Stat Tutor
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1:46

### Question 1.1

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Incorrect. If p1 = p2, then p1 - p2 = 0.
Correct. If p1 = p2, then p1 - p2 = 0.
Incorrect. Try again.
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3:28

### Question 1.2

Incorrect. Because we assume Ho: p1 = p2 is true, we can use the marginal, $$\widehat{p}$$, as our estimates of both p1 and p2.
Correct. Because we assume Ho: p1 = p2 is true, we can use the marginal, $$\widehat{p}$$, as our estimates of both p1 and p2.
Incorrect. Try again.
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3:54

### Question 1.3

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Incorrect. $$\frac{40+30}{100+100}$$ = $$\frac{70}{200}$$ = 0.35
Correct. $$\frac{40+30}{100+100}$$ = $$\frac{70}{200}$$ = 0.35
Incorrect. Try again.
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5:13

### Question 1.4

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Incorrect. $$n_{1}\widehat{p} \geq 5$$, $$n_{1}(1 - \widehat{p}) \geq 5$$, $$n_{2}\widehat{p} \geq 5$$, and $$n_{2}(1 - \widehat{p}) \geq 5$$ is the other necessary condition. These requirements for sample size must be met in order to use the z-score to find P-value using the standard Normal table.
Correct. $$n_{1}\widehat{p} \geq 5$$, $$n_{1}(1 - \widehat{p}) \geq 5$$, $$n_{2}\widehat{p} \geq 5$$, and $$n_{2}(1 - \widehat{p}) \geq 5$$ is the other necessary condition. These requirements for sample size must be met in order to use the z-score to find P-value using the standard Normal table.
Incorrect. Try again.
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6:00

### Question 1.5

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Incorrect. We want to test whether aspirin reduces the heart attack rate. So, we want the alternative hypothesis to say the heart attack rate for those taking aspirin is less than the heart attack rate of those taking a placebo.
Correct. We want to test whether aspirin reduces the heart attack rate. So, we want the alternative hypothesis to say the heart attack rate for those taking aspirin is less than the heart attack rate of those taking a placebo.
Incorrect. Try again.
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7:05

### Question 1.6

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Incorrect. $$\widehat{p}_{1}$$ = $$\frac{count\ in\ aspirin\ group\ who\ had\ heart\ attack}{count\ of\ doctors\ in\ aspirin\ group}$$ = $$\frac{104}{11037}$$
Correct. $$\widehat{p}_{1}$$ = $$\frac{count\ in\ aspirin\ group\ who\ had\ heart\ attack}{count\ of\ doctors\ in\ aspirin\ group}$$ = $$\frac{104}{11037}$$
Incorrect. Try again.
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8:52

### Question 1.7

Incorrect. This study is a completely randomized experiment. The doctors were randomly assigned to the two treatment groups.
Correct. This study is a completely randomized experiment. The doctors were randomly assigned to the two treatment groups.
Incorrect. Try again.
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9:37

### Question 1.8

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Incorrect. $$\widehat{p}$$ is the heart attack rate for all doctors in the study and equals 0.013.
Correct. $$\widehat{p}$$ is the heart attack rate for all doctors in the study and equals 0.013.
Incorrect. Try again.
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9:40

### Question 1.9

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Incorrect. A z-score of -5.14 is off the standard Normal table; the area of a standard Normal curve less than z = –5.14 is essentially zero.
Correct. A z-score of -5.14 is off the standard Normal table; the area of a standard Normal curve less than z = –5.14 is essentially zero.
Incorrect. Try again.
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9:52

### Question 1.10

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Incorrect. P-value = 0.000 is less than $$\alpha$$ = 0.05, so we reject H0.
Correct. P-value = 0.000 is less than $$\alpha$$ = 0.05, so we reject H0.
Incorrect. Try again.
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10:47

### Question 1.11

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Incorrect. Since this was a valid experiment and the results are significant, we can conclude causation.
Correct. Since this was a valid experiment and the results are significant, we can conclude causation.
Incorrect. Try again.
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