Chapter 10: Q. 72. (page 672)
Based on the P-value in Exercise 71, which of the following must be true?
a. A confidence interval for μM−μFwill contain
b. A confidence interval for μM−μFwill contain
c. A confidence interval for μM−μFwill contain
d. A confidence interval for μM−μF will contain
The required correct option is
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Bag lunch? Phoebe has a hunch that older students at her very large high
school are more likely to bring a bag lunch than younger students because they have grown tired of cafeteria food. She takes a simple random sample of 80 sophomores and finds that of them bring a bag lunch. A simple random sample of seniors reveals that of them bring a bag lunch.
a. Do these data give convincing evidence to support Phoebe’s hunch at the significance level?
b. Interpret the -value from part (a) in the context of this study.
A researcher wished to compare the average amount of time spent in extracurricular activities by high school students in a suburban school district with that in a school district of a large city. The researcher obtained an SRS of high school students in a large suburban school district and found the mean time spent in extracurricular activities per week to be hours with a standard deviation of hours. The researcher also obtained an independent SRS of high school students in a large city school district and found the mean time spent in extracurricular activities per week to be hours with a standard deviation of hours. Suppose that the researcher decides to carry out a significance test of : μsuburban=μcity versus a two-sided alternativ
The P-value for the test is . A correct conclusion is to
a. fail to reject because. There is convincing evidence of a difference in the average time spent on extracurricular activities by students in the suburban and city school districts.
b. fail to reject because . There is not convincing evidence of a difference in the average time spent on extracurricular activities by students in the suburban and city school districts.
c. fail to reject because. There is convincing evidence that the average time spent on extracurricular activities by students in the suburban and city school districts is the same.
d. reject because . There is not convincing evidence of a difference in the average time spent on extracurricular activities by students in the suburban and city school districts.
e. reject because . There is convincing evidence of a difference in the average time spent on extracurricular activities by students in the suburban and city school districts.
Music and memory Does listening to music while studying help or hinder students’ learning? Two statistics students designed an experiment to find out. They selected a random sample of students from their medium-sized high school to participate. Each subject was given minutes to memorize two different lists of words, once while listening to music and once in silence. The order of the two word lists was determined at random; so was the order of the treatments. The difference (Silence − Music) in the number of words recalled was recorded for each subject. The mean difference was and the standard deviation of the differences was .
a. If the result of this study is statistically significant, can you conclude that the difference in the ability to memorize words was caused by whether students were performing the task in silence or with music playing? Why or why not?
b. Do the data provide convincing evidence at the significance level that the number of words recalled in silence or when listening to music differs, on average, for students at this school?
c. Based on your conclusion in part (a), which type of error—a Type I error or a Type II error—could you have made? Explain your answer.
Broken crackers We don’t like to find broken crackers when we open the package. How can makers reduce breaking? One idea is to microwave the crackers for seconds right after baking them. Randomly assign newly baked crackers to the microwave and another to a control group that is not microwaved. After day, none of the microwave group were broken and of the control group were broken. Let be the true proportions of crackers like these that would break if baked in the microwave and be the true proportions of crackers like these that would break if not microwaved. Check if the conditions for calculating a confidence interval formet.
A random sample of of last year’s model of a certain popular car found that had a specific minor defect in the brakes. The automaker adjusted the production process to try to reduce the proportion of cars with the brake problem. A random sample of of this year’s model found that had the minor brake defect.
a. Was the company’s adjustment successful? Carry out an appropriate test to support your answer. b. Based on your conclusion in part (a), which mistake—a Type I error or a Type II error—could have been made? Describe a possible consequence of this error.
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