Chapter 1. Significance Tests for a Proportion

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.

2

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.

2

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

Incorrect. Data should be collected with a simple random sample.

Correct. Data should be collected with a simple random sample.

Incorrect. Try again.

2

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.

2

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.

2

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.

2

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.

2

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.

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2

Incorrect. Since we rejected H₀, we conclude that H_a is correct. Thus the proportion differs significantly from 0.73.

Correct. Since we rejected H₀, we conclude that H_a is correct. Thus the proportion differs significantly from 0.73.

Incorrect. Try again.

2

Incorrect. \(\widehat{p} \) = \(\frac{40}{6000}\) = 0.0067

Correct. \(\widehat{p} \) = \(\frac{40}{6000}\) = 0.0067

Incorrect. Try again.

2

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

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.

2