Question

1.

According to the National Institute on Drug Abuse, a U.S. government agency, 17.3% of 8th graders in 2010 had used marijuana at some point in their lives. A school official hopes to show the percentage is lower in his district, testing H0: p = 0.173 versus Ha: p < 0.173.

The health department for the district uses anonymous random sampling and finds that 10% of 80 eighth graders surveyed had used marijuana.

Is the sample size condition for conducting a hypothesis test for a population proportion satisfied?

A. No, because (80)(.10) is less than 10. Because of this the sample size is too small to use the normal distribution to model the distribution of sample proportions.

B. No, because 80 students is not enough to be representative of the students in the school district.

C. Yes, because the sample is random. It represents the 8th graders in the district.

D. Yes, because (80)(.173) and (80)(1 ‑ 0.173) are both at least 10. This means we can use the normal distribution to model the distribution of sample proportions.

2.

A 2014 study by the reputable Gallup organization estimates that 44% of U.S. adults are underemployed. Underemployed means the person wants to work full time but is employed part time or unemployed. We want to know if the proportion is smaller this year. We select a random sample of 100 U.S. adults this year and find that 40% are underemployed.

After carrying out the hypothesis test for p = 0.44 compared to p < 0.44, we obtain a P‑value of 0.21. Which of the following interpretations of the P‑value is correct?

A. There is a 21% chance that 44% of U.S. adults are underemployed this year

B. There is a 21% chance that 40% of U.S. adults are underemployed this year.

C. There is a 21% chance that 40% or fewer U.S. adults are underemployed this year if 44% were underemployed in 2014.

D. There is a 21% chance that a sample of 100 U.S. adults will have 40% or fewer underemployed if 44% of the population is underemployed this year.

3.

Coffee: A popular chain of cafes has been receiving online complaints about one store location. Regular customers complained that the staff at this location consistently underfill their cups of coffee. The owner of the chain will personally visit the location to meet with the staff if more than 10% of the 16 ounce cups are underfilled by 1 fluid ounce. She arranges to have “mystery shoppers” visit the store. Mystery shoppers are people who are paid to pose as a regular customer and provide feedback to the owner about customer service.

After 100 mystery shop visits, she finds that 18 of the 16 ounce cups of coffee were underfilled. She plans to test the hypotheses H0: p = 0.10 versus Ha: p > 0.10.

What is the test statistic?

A. Z = 2.67

B. Z = -2.67

C. Z = -2.08

D. Z = 2.08

Answer 1