Chapter 9: Q .1. (page 563)
No homework? Mr. Tabor believes that less than of the students at his school completed their math homework last night. The math teachers inspect the homework assignments from a random sample of students at the school.
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A researcher claims to have found a drug that causes people to grow taller. The coach of the basketball team at Brandon University has expressed interest but demands evidence. Over 1000 Brandon students volunteer to participate in an experiment to test this new drug. Fifty of the volunteers are randomly selected, their heights are measured, and they are given the drug. Two weeks later, their heights are measured again. The power of the test to detect an average increase in height of 1 inch could be increased by
a. using only volunteers from the basketball team in the experiment.
b. using instead of
c. using instead of
d. giving the drug to 25 randomly selected students instead of .
e. using a two-sided test instead of a one-sided test.
Potato chips A company that makes potato chips requires each shipment of
potatoes to meet certain quality standards. If the company finds convincing evidence that more than of the potatoes in the shipment have “blemishes,” the truck will be sent back to the supplier to get another load of potatoes. Otherwise, the entire truckload will be used to make potato chips. To make the decision, a supervisor will inspect a random sample of potatoes from the shipment. He will then perform a test of versus , where p is the true proportion of potatoes with blemishes in a given truckload. The power of the test to detect that , based on a random sample of potatoes and significance level , is Interpret this value.
More lefties?In the population of people in the United States, about 10% are left-handed. After bumping elbows at lunch with several left-handed students, Simon wondered if more than of students at his school are left-handed. To investigate, he selected an SRS of students and found lefties .
To determine if these data provide convincing evidence that more than of the students at Simon’s school are left-handed, trials of a simulation were conducted. Each dot in the graph shows the proportion of students that are left-handed in a random sample of students, assuming that each student has a chance of being left handed.
a. State appropriate hypotheses for performing a significance test. Be sure to define the parameter of interest.
b. Use the simulation results to estimate the P-value of the test in part (a). Interpret the -value.
c. What conclusion would you make?
Opening a restaurant You are thinking about opening a restaurant and are
searching for a good location. From research you have done, you know that the mean income of those living near the restaurant must be over to support the type of upscale restaurant you wish to open. You decide to take a simple random sample of people living near one potential location. Based on the mean income of this sample, you will perform a test of
where is the true mean income in the population of people who live near the restaurant. Describe a Type error and a Type error in this setting, and give a possible consequence of each.
Proposition XA political organization wants to determine if there is convincing evidence that a majority of registered voters in a large city favor Proposition X. In an SRS of registered voters, favor the proposition. Explain why it isn’t necessary to carry out a significance test in this setting.
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