# AP Statistics Multiple-Choice Practice Questions: Tests of Significance-Proportions and Means 1

### Test Information

13 questions

30 minutes

1. Which of the following is a true statement?

2. Which of the following is a true statement?

3. Question below refers to the following:

Video arcades provide a vehicle for competition and status within teenage peer groups and are recognized as places where teens can hang out and meet their friends. The national PTA organization, concerned about the time and money being spent in video arcades by middle school students, commissions a statistical study to investigate whether or not middle school students are spending an average of over two hours per week in video arcades. Twenty communities are randomly chosen, five middle schools are randomly picked in each of the communities, and ten students are randomly interviewed at each school.

What is the parameter of interest?

4. Question below refers to the following:

Video arcades provide a vehicle for competition and status within teenage peer groups and are recognized as places where teens can hang out and meet their friends. The national PTA organization, concerned about the time and money being spent in video arcades by middle school students, commissions a statistical study to investigate whether or not middle school students are spending an average of over two hours per week in video arcades. Twenty communities are randomly chosen, five middle schools are randomly picked in each of the communities, and ten students are randomly interviewed at each school.

What are the null and alternative hypotheses which the PTA is testing?

5. A hypothesis test comparing two population proportions results in a P-value of 0.032. Which of the following is a proper conclusion?

6. A company manufactures a synthetic rubber (jumping) bungee cord with a braided covering of natural rubber and a minimum breaking strength of 450 kg. If the mean breaking strength of a sample drops below a specified level, the production process is halted and the machinery inspected. Which of the following would result from a Type I error?

7. One ESP test asks the subject to view the backs of cards and identify whether a circle, square, star, or cross is on the front of each card. If p is the proportion of correct answers, this may be viewed as a hypothesis test with H0: p = 0.25 and Ha: p > 0.25. The subject is recognized to have ESP when the null hypothesis is rejected. What would a Type II error result in?

8. A coffee-dispensing machine is supposed to deliver 12 ounces of liquid into a large paper cup, but a consumer believes that the actual amount is less. As a test he plans to obtain a sample of 5 cups of the dispensed liquid and if the mean content is less than 11.5 ounces, to reject the 12-ounce claim. If the machine operates with a known standard deviation of 0.9 ounces, what is the probability that the consumer will mistakenly reject the 12-ounce claim even though the claim is true? (Assume that all conditions for inference are met.)

9. A pharmaceutical company claims that a medicine will produce a desired effect for a mean time of 58.4 minutes. A government researcher runs a hypothesis test of 40 patients and calculates a mean of = 59.5 with a standard deviation of s = 8.3. What is the P-value?

10. You plan to perform a hypothesis test with a level of significance of α = 0.05. What is the effect on the probability of committing a Type I error if the sample size is increased?

11. A fast food chain advertises that their large bag of french fries has a weight of 150 grams. Some high school students, who enjoy french fries at every lunch, suspect that they are getting less than the advertised amount. With a scale borrowed from their physics teacher, they weigh a random sample of 15 bags. What is the conclusion if the sample mean is 145.8 g and standard deviation is 12.81 g? (Assume that all conditions for inference are met.)

12. A researcher believes a new diet should improve weight gain in laboratory mice. If ten control mice on the old diet gain an average of 4 ounces with a standard deviation of 0.3 ounces, while the average gain for ten mice on the new diet is 4.8 ounces with a standard deviation of 0.2 ounces, what is the P-value? (Assume that all conditions for inference are met.)

13. A school superintendent must make a decision whether or not to cancel school because of a threatening snow storm. What would the results be of Type I and Type II errors for the null hypothesis: The weather will remain dry?