Chapter 9 MC Test Review

Which of the following best describes a Type I error?

• (a) concluding the dryer is not dented or scratched when it really is

• (b) concluding the dryer is not dented or scratched when it really is not

• (c) concluding the dryer is dented or scratched when it really is

• (d) concluding the dryer is dented or scratched when it really is not

• (e) It is not possible to make a Type I error in this situation.

A manager wants to determine the proportion of employees that arrive to work late. She will call a company meeting if there is clear evidence that this proportion is greater than 0.10. She selects a random sample of 30 employees from the 500 employees at this company to test the hypotheses H_0: p = 0.10, H_a: p > 0.10. Which condition for inference has not been met in this situation, if any?

• The data are a random sample from the population of interest.

• The sample size is less than 10% of the population size.

• np ≥ 10 and n(1 - p) ≥ 10

• None of the conditions are violated.

• More than one condition is violated.

A buyer for a grocery chain inspects large truckloads of apples to determine the proportion p of apples in the shipment that are rotten. She will only accept the shipment if there is clear evidence that this proportion is less than 0.06. She selects a random sample of 200 apples from the over 20,000 apples on the truck to test the hypotheses H_0: p = 0.06, H_a: p < 0.06. The sample contains 9 rotten apples. Which of the following intervals contains the P-value for this test?

• greater than 0.10

• between 0.10 and 0.05

• between 0.05 and 0.025

• between 0.025 and 0.01

• less than 0.01

• 0.90

• 0.40

• 0.05

• 0.20

• 0.10

Which of the following increases the power of a significance test?

• Using a two-tailed test instead of a one-tailed test.

• Decreasing the size of your sample.

• Perform the test many times using the same data.

A sociologist is studying the effect of having children within the first two years of marriage on the divorce rate.  Using hospital birth records, she selects a random sample of 200 couples who had a child within the first two years of marriage.  Following up on these couples, she finds that 80 couples are divorced within five years.

To determine if having children within the first two years of marriage increases the divorce rate we should test

• hypotheses H₀: p = 0.50, H_a: p  0.50.

• hypotheses H₀: p = 0.50, H_a: p > 0.50.

• hypotheses H₀: p = 0.50, H_a: p < 0.50.

• hypotheses H₀: p = 0.40, H_a: p > 0.40.

• none of the other options.

An inspector inspects large truckloads of potatoes to determine the proportion p in the shipment with major defects prior to using the potatoes to make potato chips.  Unless there is clear evidence that this proportion is less than 0.10, she will reject the shipment.  To reach a decision she will test the hypotheses          

H₀: p = 0.10, H_a: p < 0.10 using the large-sample test for a population proportion.  To do so, she selects an SRS of 50 potatoes from the more than 2000 potatoes on the truck.  Suppose that only two of the potatoes sampled are found to have major defects.

Which of the following conditions for inference about a proportion using a hypothesis test are violated?

• The data are an SRS from the population of interest.

• The population is at least 10 times as large as the sample.

• n is so large that both np₀ and n(1 – p₀) are 10 or more, where p₀ is the proportion with major defects if the null hypothesis is true.

• There appear to be no violations.

• More than one condition is violated.

Is the proportion of marshmallows in Mr. Miller’s favorite breakfast cereal lower than it used to be? To   determine this, you test the hypotheses Ho: p _old = p _new, Ha: p _old > p _new at the α = 0.05 level. You calculate a test statistic of 1.980. Which of the following is the appropriate P-value and conclusion for your test?

• P-value = 0.047; fail to reject Ho; we do not have convincing evidence that the proportion of marshmallows has been reduced

• P- value = 0.047; accept Ha; there is convincing evidence that the proportion of marshmallows has been reduced

• P-value = 0.024; fail to reject Ho; we do not have convincing evidence that the proportion of marshmallows has been reduced

• P-value= 0.024; reject Ho; we have convincing evidence that the proportion of marshmallows has been reduced

• P-value = 0.024; fail to reject Ho; we have convincing evidence that the proportion of marshmallows has not changed

Which of the following 95% confidence intervals would lead us to reject H₀: p = 0.30 in favor of H_a: p ≠ 0.30 at the 5% significance level?

• (0.30, 0.38)

• (0.19, 0.27)

• (0.27, 0.31)

• (0.24, 0.30)

• None of these