AP Statistics 9.1 and 9.2

To determine if having children within the first two years of marriage increases the divorce rate, where p = proportion of marriages that end in divorce, we should test the hypotheses

• H_o:  p̂ = 0.5; H_a: p̂ ≠ 0.5
• H_o:  p̂ = 0.5; H_a: p̂ > 0.5
• H_o:  p > 0.5; H_a: p = 0.5
• H_o:  p = 0.5; H_a: p > 0.5

In their advertisements, a new diet program would like to claim that their methods result in a mean weight loss of more than ten pounds in two weeks. In order to determine if this is a valid claim, they hire an independent testing agency that then selects twenty-five people to be placed on this diet. The agency should be testing the null hypothesis H₀: m = 10 and the alternative hypothesis (m = mean weight loss)

• Ha: μ < 10

• Ha: μ > 10

• Ha: μ ≥ 10

• Ha: μ ≤ 10

The average growth of a certain variety of pine tree is 10.1 inches in three years. A biologist claims that a new variety will have a greater three-year growth. A random sample of 25 of the new variety has an average three-year growth of 10.8 inches and a standard deviation of 2.1 inches.  The appropriate null and alternative hypotheses to test the biologist's claim are

• H₀: µ = 10.8 against H_a: µ > 10.8
• H₀: µ = 10.8 against H_a: µ 10.8
• H₀: µ = 10.1 against H_a: µ > 10.1
• H₀: µ = 10.1 against H_a: µ < 10.1

The P-value of a test of a null hypothesis is the probability that

• assuming the null hypothesis is true, the test statistic will take a value at least as extreme as that actually observed.
• assuming the null hypothesis is false, the test statistic will take a value at least as extreme as that actually observed.
• the null hypothesis is true.
• the null hypothesis is false.

In testing hypotheses, which of the following would be strong evidence against the null hypothesis?

• Using a small level of significance
• Using a large level of significance
• Obtaining data with a small P-value
• Obtaining data with a large P-value

I conduct a statistical test of hypotheses and find that the null hypothesis is statistically significant at level a = 0.05. I may conclude that

• the test would also be significant at level a = 0.10.

• the test would also be significant at level a = 0.01.

• the P-value is less than .05.

• both (A) and (C) are true.

• (A), (B), and (C) are all correct

A test of significance produces a P-value of 0.024.  Which of the following conclusions is appropriate?

• Accept H_a at the α = 0.05 level
• Reject H_a at the α = 0.01 level
• Fail to reject H₀ at the α = .05 level
• Reject H₀ at the α = 0.05 level

If we reject the null hypothesis when, in fact, it is true, we have

• committed a Type I error.
• committed a Type II error.
• a probability of being correct that is equal to the P-value.
• a probability of being correct that is equal to 1 – P-value.

A Type II error is

• rejecting the null hypothesis when it is true.
• failing to reject the null hypothesis when it is false.
• incorrectly specifying the null hypothesis.
• incorrectly specifying the alternative hypothesis.

A researcher plans to conduct a test of hypotheses at the a = 0.01 significance level. She designs her study to have a power of 0.90 at a particular alternative value of the parameter of interest. The probability that the researcher will commit a Type I error is

• 0.01
• 0.10
• 0.89
• 0.90