Hypothesis Testing of Mean & Proportion

Chapter 8, Section 2

Problem 22

Finding critical values - Assume that the normal distribution applies and find the critical z values.

x = 0.01; H1 is p > 0.5

Problem 28

Finding Test Statistics - Find the value of the test statistic z using

Seat Belts - The claim is that more than 75% of adults always wear a seat belt in the front seat. A Harris Poll of 1012 adults resulted in 870 who say that they always wear a seat belt in the front seat.

Problem 46

Interpreting Power - Chantix tablets are used as an aid to help people stop smoking. In a clinical trial, 129 subjects were treated with Chantix twice a day for 12 weeks, and 16 subjects experienced abdominal pain (based on data from Pfizer, Inc.). If someone claims that more than 8% of Chantix users experience abdominal pain, that claim is supported with a hypothesis test conducted with a 0.05 significance level. Using 0.18 as an alternative value of p, the power of the test is 0.96. Interpret this value of the power of the test.

Chapter 8, Section 3

Problem 6

Identify the indicated values or interpret the given display. Use the normal distribution as an approximation to the binomial distribution (as described in Part of this section).

Driving and Texting - In a survey, 1864 out of 2246 randomly selected adults in the U.S. said that texting while driving should be illegal (based on data from Zogby International). Consider a hypothesis test that uses a 0.05 significance level to test the claim that more than 80% of adults believe that texting while driving should be illegal.

a. What is the test statistic?

b. What is the critical value?

c. What is the P-value?

d. What is the conclusion?

Problem 18

Testing Claims About Proportions - Test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that address the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution (as described in Part 1 of this section).

Gender Selection for Boys - The Genetics and IVF Institute conducted a clinical trial of the YSORT method designed to increase the probability that a baby is a boy. As of this writing, among the babies born to parents using the YSORT method, 172 were boys and 39 were girls. Use the sample data with 0.01 significance level to test the claim that with this method, the probability of a baby being a boy is greater than 0.5. Does the YSORT method of gender selection appear to work?

Problem 28

Bias in Jury Selection - In the case of Casteneda v. Partida, it was found that during a period of 11 years in Hidalgo County, Texas, 870 people were selected for grand jury duty, and 39% of them were Americans of Mexican ancestry. Among the people eligible for grand jury duty, 79.1% were Americans of Mexican ancestry. Use a 0.01 significance level to test the claim that the selection process is biased against Americans of Mexican ancestry. Does the jury selection system appear to be fair?

Chapter 8, Section 4

Problem 12

Testing Hypotheses - Identify the null hypothesis, alternative hypothesis, test statistics, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that address the original claim. Use the P-value method unless your instructor specifies otherwise.

Loaded Die - When a fair die is rolled many times, the outcomes of 1, 2, 3, 4, 5 and 6 are equally likely, so the mean of the outcomes should be 3.5. The author drilled holes into a die and loaded it by inserting lead weights, then rolled it 16 times to obtain a mean of 2.9375.

Assume that the standard deviation of the outcomes is 1.7078, which is the standard deviation for a fair die. Use a 0.05 significance level to test the claim that outcomes from the loaded die have a mean different from the value of 3.5 expected with a fair die. Is there anything about the sample data suggesting that the methods of this section should not be used?

Problem 20

Using Raw Data - Test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that address the original claim. Use the P-value method unless your instructor specifies otherwise.

California Speeding - Listed below are recorded speeds in (in mi/h) of randomly selected cars traveling on a section of Highway 405 in Los Angeles (based on data from Sigalert). That part of the highway has a posted speed limit of 65 mi/h. Assume that the standard deviation of speeds is 5.7 mi/h and use a 0.01 significance level to test the claim that the sample is from a population with a mean that is greater than 65 mi/h.

68 68 72 73 65 74 73 72 68 65 65 73 66 71 68 74 66 71 65 73

59 75 70 56 66 75 68 75 62 72 60 73 61 75 58 74 60 73 58 75