Hypothesis Test AP Statistics Scofield

Which of the following represents the appropriate null & alternative hypotheses? The mean height of women is greater than 64"

• H₀: μ > 64"

  Hₐ: μ ≠ 64"

• H₀: μ < 64"

  Hₐ: μ > 64"

• H₀: p > 64"

  Hₐ: p ≠ 64"

• H₀: p = 64"

  Hₐ: p > 64"

Suppose the P-value for a hypothesis test is 0.0304. Using a = 0.05, what is the appropriate conclusion?

• Reject the null hypothesis

• Reject the alternative hypothesis

• Fail to reject the null hypothesis

• Fail to reject the alternative hypothesis

A mayor is concerned about the percentage of city residents who express disapproval of his job performance. His political committee pays for a newspaper ad, hoping to keep his disapproval rating below 21%. They will use a follow up poll to access effectiveness. What are the correct null and alternative hypotheses?

• Ho: μ > 21

  Ha: μ < 21

• Ho: p > .20

  Ha: p < .20

• Ho: p < .21

  Ha: p > .21

• Ho: p > .21

  Ha: p < .21

The weight of the average 6th grade student's backpack (with books in it) is 18.4 lbs. The principal of the school thinks that the backpack does not weight 18.4 lbs. What is the null and alternate hypothesis?

• H₀ = 18.4
  H_a = 18.4

• H₀ = 18.4
  H_a > 18.4

• H₀ = 18.4
  H_a < 18.4

• H₀ = 18.4
  H_a ≠ 18.4

A company that ships glass for a glass manufacturer claimed that its shipping boxes are constructed so that no more than 8 percent of the boxes arrive with broken glass. The glass manufacturer believed the actual percent is greater than 8 percent. The manufacturer selected a random sample of boxes and recorded the proportion of boxes that arrived with broken glass. The manufacturer tested the hypotheses H_o:p=0.08 versus H_a:p>0.08 at the significance level of α=0.01 . The test yielded a p-value of 0.001. Assuming all conditions for inference were met, which of the following is the correct conclusion?

• The p-value is greater than α, and the null hypothesis is rejected. There is convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08.

• The p-value is greater than α, and the null hypothesis is rejected. There is not convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08.

• The p-value is greater than α, and the null hypothesis is not rejected. There is not convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08.

• The p-value is less than α, and the null hypothesis is rejected. There is convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08.

• The p-value is less than α, and the null hypothesis is not rejected. There is not convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08.

Answer explanation

The null hypothesis is rejected because the p-value (0.001) is less than α=0.01. There is convincing evidence to support the alternative hypothesis that the population proportion is greater than 0.08.

A factory manager selected a random sample of parts produced on an old assembly line and a random sample of parts produced on a new assembly line. The difference between the sample proportion of defective parts made on the old assembly line and the sample proportion of defective parts made on the new assembly line (old minus new) was 0.006. Under the assumption that all conditions for inference were met, a hypothesis test was conducted with the alternative hypothesis being the proportion of defective parts made on the old assembly line is greater than that of the new assembly line. The p-value of the test was 0.018. Which of the following is the correct interpretation of the p-value?

• If there is a difference of 0.018 in the proportions of all defective parts made on the two assembly lines, the probability of observing that difference is 0.006.

• If there is a difference of 0.006 in the proportions of all defective parts made on the two assembly lines, the probability of observing that difference is 0.018.

• If there is no difference in the proportions of all defective parts made on the two assembly lines, the probability of observing a difference equal to 0.006 is 0.018.

• If there is no difference in the proportions of all defective parts made on the two assembly lines, the probability of observing a difference of at least 0.006 is 0.018.

• If there is no difference in the proportions of all defective parts made on the two assembly lines, the probability of observing a difference of at most 0.006 is 0.018

Answer explanation

The direction of the test is to the right of 0.006, because the alternative hypothesis is that the proportion of defective parts on the old line is greater than the proportion of defective parts on the new line. The test is in the direction of the right tail. The -value is the probability of observing a sample difference of at least 0.006 if the null hypothesis of no difference is true.

Which of the following is a true statement?

• Tests of significance (hypothesis tests) are designed to measure the strength of evidence against the null hypothesis.

• A well-planned test of significance should result in a statement either that the null hypothesis is true or that it is false.

• The null hypothesis is one-sided and expressed using either < or > if there is interest in deviations in only one direction.

• When a true parameter value is farther from the hypothesized value, it becomes easier to reject the alternative hypothesis.

• Increasing the sample size makes it more difficult to conclude that an observed difference between observed and hypothesized values is significant.

A test of H₀: µ=60 (claim) and H_a: µ≠60 produces a P-value of 0.04. Using α = 0.05, which of the following is an appropriate conclusion?

• There is enough evidence to support the claim.

• There is not enough evidence to support the claim.

• There is not enough evidence to reject the claim.

• There is enough evidence to reject the claim.

Which of the following is a true statement?

• Tests of significance (hypothesis tests) are designed to measure the strength of evidence against the null hypothesis.

• A well-planned test of significance should result in a statement either that the null hypothesis is true or that it is false.

• The null hypothesis is one-sided and expressed using either < or > if there is interest in deviations in only one direction.

• When a true parameter value is farther from the hypothesized value, it becomes easier to reject the alternative hypothesis.

• Increasing the sample size makes it more difficult to conclude that an observed difference between observed and hypothesized values is significant.

It is a statistical method applied in making decisions using experimental data. Hypothesis testing is basically testing an assumption that we make about a population.

• conclusion

• hypothesis testing

• hypothesis

• proposition