# Chapter 1. Significance Tests for a Proportion

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Stat Tutor
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1:05

### Question 1.1

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Incorrect. This is true provided np and n(1 - p) are both bigger than 10.
Correct. This is true provided np and n(1 - p) are both bigger than 10.
Incorrect. Try again.
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1:10

### Question 1.2

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Incorrect. The problem is that we don't know the value of p. That's why we are performing a test of significance. Note: We can get the value of $$\widehat{p}$$ from the sample and the value of $$p_{o}$$ from the null hypothesis.
Correct. The problem is that we don't know the value of p. That's why we are performing a test of significance. Note: We can get the value of $$\widehat{p}$$ from the sample and the value of $$p_{o}$$ from the null hypothesis.
Incorrect. Try again.
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3:45

### Question 1.3

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Incorrect. Since we assume the null hypothesis to be true, we assume that $$p= p_{o}$$ so we use $$p_{o}$$ as the value of p whenever we need a value for p.
Correct. Since we assume the null hypothesis to be true, we assume that $$p= p_{o}$$ so we use $$p_{o}$$ as the value of p whenever we need a value for p.
Incorrect. Try again.
2

4:51

### Question 1.4

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Incorrect. Data should be collected with a simple random sample.
Correct. Data should be collected with a simple random sample.
Incorrect. Try again.
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5:32

### Question 1.5

Incorrect. The response variable is a measure on the individual. Each student is asked whether they feel "being very well-off financially is an important personal goal," so that is the response variable and it is categorical.
Correct. The response variable is a measure on the individual. Each student is asked whether they feel "being very well-off financially is an important personal goal," so that is the response variable and it is categorical.
Incorrect. Try again.
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### Question 1.6

Incorrect. The research question basically asks, "Is the proportion . . . significantly different from . . .73%?" Thus, the alternative hypothesis is p $$\neq$$ 0.73.
Correct. The research question basically asks, "Is the proportion . . . significantly different from . . .73%?" Thus, the alternative hypothesis is p $$\neq$$ 0.73.
Incorrect. Try again.
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6:19

### Question 1.7

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Incorrect. Whenever the response variable is categorical, we do inference on proportion.
Correct. Whenever the response variable is categorical, we do inference on proportion.
Incorrect. Try again.
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6:47

### Question 1.8

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Incorrect. Since we assume the null hypothesis to be true, we assume that $$p= p_{o}$$ = 0.73 so we use $$p_{o}$$ = 0.73 and check $$n p_{o} \geq 10$$ and $$n(1- p_{o} ) \geq 10$$ to see if n is large enough.
Correct. Since we assume the null hypothesis to be true, we assume that $$p= p_{o}$$ = 0.73 so we use $$p_{o}$$ = 0.73 and check $$n p_{o} \geq 10$$ and $$n(1- p_{o} ) \geq 10$$ to see if n is large enough.
Incorrect. Try again.
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9:22

### Question 1.9

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Incorrect. Because P-value = 0.0258 is less than $$\alpha$$ = 0.05, we reject H0.
Correct. Because P-value = 0.0258 is less than $$\alpha$$ = 0.05, we reject H0.
Incorrect. Try again.
2

9:37

### Question 1.10

Incorrect. Since we rejected H0, we conclude that Ha is correct. Thus the proportion differs significantly from 0.73.
Correct. Since we rejected H0, we conclude that Ha is correct. Thus the proportion differs significantly from 0.73.
Incorrect. Try again.
2

11:40

### Question 1.11

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Incorrect. $$\widehat{p}$$ = $$\frac{40}{6000}$$ = 0.0067
Correct. $$\widehat{p}$$ = $$\frac{40}{6000}$$ = 0.0067
Incorrect. Try again.
2

12:42

### Question 1.12

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Incorrect. All 6,000 three- to ten-year-olds in Brick Township were studied.
Correct. All 6,000 three- to ten-year-olds in Brick Township were studied.
Incorrect. Try again.
2

17:46

### Question 1.13

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Incorrect. We use the standard Normal table to find the P-value for testing proportion.
Correct. We use the standard Normal table to find the P-value for testing proportion.
Incorrect. Try again.
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