Math 227 / Fall 2014 Instructor: David Soto Name______________________________________________ Chapter 2 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Use the traditional method to test the given hypothesis. Assume that the samples are independent and that they have been randomly selected 1) A marketing survey involves product recognition in New York and California. Of 558 1) New Yorkers surveyed, 193 knew the product while 196 out of 614 Californians knew the product. At the 0.05 significance level, test the claim that the recognition rates are the same in both states. 2) Use the given sample data to test the claim that p1 < p2 . Use a significance level of 0.10. Sample 1 Sample 2 n 1 = 462 n 2 = 380 x1 = 84 2) x2 = 95 3) A researcher finds that of 1000 people who said that they attend a religious service at least 3) 4) In a random sample of 360 women, 65% favored stricter gun control laws. In a random 4) 5) In a random sample of 500 people aged 20-24, 22% were smokers. In a random sample of 5) 6) Seven of 8500 people vaccinated against a certain disease later developed the disease. 18 6) once a week, 31 stopped to help a person with car trouble. Of 1200 people interviewed who had not attended a religious service at least once a month, 22 stopped to help a person with car trouble. At the 0.05 significance level, test the claim that the two proportions are equal. sample of 220 men, 60% favored stricter gun control laws. Test the claim that the proportion of women favoring stricter gun control is higher than the proportion of men favoring stricter gun control. Use a significance level of 0.05. 450 people aged 25-29, 14% were smokers. Test the claim that the proportion of smokers in the two age groups is the same. Use a significance level of 0.01. of 10,000 people vaccinated with a placebo later developed the disease. Test the claim that the vaccine is effective in lowering the incidence of the disease. Use a significance level of 0.02. 1 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Construct the indicated confidence interval for the difference between population proportions p1 - p2 . Assume that the samples are independent and that they have been randomly selected. 7) A marketing survey involves product recognition in New York and California. Of 558 New Yorkers surveyed, 193 knew the product while 196 out of 614 Californians knew the product. Construct a 99% confidence interval for the difference between the two population proportions. A) -0.0177 < p1 - p2 < 0.1243 B) -0.0034 < p1 - p2 < 0.0566 C) 0.0247 < p1 - p2 < 0.0286 7) D) -0.0443 < p1 - p2 < 0.0976 8) In a random sample of 300 women, 45% favored stricter gun control legislation. In a random 8) sample of 200 men, 25% favored stricter gun control legislation. Construct a 98% confidence interval for the difference between the population proportions p1 - p2 . A) 0.102 < p1 - p2 < 0.298 C) 0.092 < p1 - p2 < 0.308 B) 0.118 < p1 - p2 < 0.282 D) 0.114 < p1 - p2 < 0.286 Determine whether the samples are independent or dependent. 9) The effectiveness of a new headache medicine is tested by measuring the amount of time before the headache is cured for patients who use the medicine and another group of patients who use a placebo drug. A) Independent samples B) Dependent samples 9) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Test the indicated claim about the means of two populations. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Use the traditional method or P-value method as indicated. 10) Two types of flares are tested and their burning times (in minutes) are recorded. The 10) summary statistics are given below. Brand X Brand Y n = 35 n = 40 x = 19.4 min s = 1.4 min x = 15.1 min s = 0.8 min Use a 0.05 significance level to test the claim that the two samples are from populations with the same mean. Use the traditional method of hypothesis testing. 2 11) A researcher was interested in comparing the GPAs of students at two different colleges. 11) Independent random samples of 8 students from college A and 13 students from college B yielded the following GPAs: College A College B 3.7 3.8 2.8 3.2 3.2 4.0 3.0 3.0 3.6 2.5 3.9 2.6 2.7 3.8 4.0 3.6 2.5 3.6 2.8 3.9 3.4 Use a 0.10 significance level to test the claim that the mean GPA of students at college A is different from the mean GPA of students at college B. Use the P-value method of hypothesis testing. (Note: x1 = 3.1125, x2 = 3.4385, s1 = 0.4357, s2 = 0.5485.) 12) A researcher wishes to determine whether people with high blood pressure can reduce 12) their blood pressure, measured in mm Hg, by following a particular diet. Use a significance level of 0.01 to test the claim that the treatment group is from a population with a smaller mean than the control group. Use the traditional method of hypothesis testing. Treatment Group Control Group n 1 = 35 n 2 = 28 x 1 = 189.1 s1 = 38.7 x2 = 203.7 s2 = 39.2 13) A researcher was interested in comparing the amount of time (in hours) spent watching television by women and by men. Independent simple random samples of 14 women and 17 men were selected, and each person was asked how many hours he or she had watched television during the previous week. The summary statistics are as follows. Women Men x1 = 12.5 hr s1 = 3.9 hr n 1 = 14 x2 = 13.8 hr s2 = 5.2 hr n 2 = 17 Use a 0.05 significance level to test the claim that the mean amount of time spent watching television by women is smaller than the mean amount of time spent watching television by men. Use the traditional method of hypothesis testing. 3 13) 14) A researcher was interested in comparing the resting pulse rates of people who exercise 14) regularly and of those who do not exercise regularly. Independent simple random samples of 16 people who do not exercise regularly and 12 people who exercise regularly were selected, and the resting pulse rates (in beats per minute) were recorded. The summary statistics are as follows. Do not exercise regularly Exercise regularly x1 = 73.0 beats/min s1 = 10.9 beats/min n 1 = 16 x2 = 68.4 beats/min s2 = 8.2 beats/min n 2 = 12 Use a 0.025 significance level to test the claim that the mean resting pulse rate of people who do not exercise regularly is larger than the mean resting pulse rate of people who exercise regularly. Use the traditional method of hypothesis testing. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the samples are independent or dependent. 15) The effectiveness of a headache medicine is tested by measuring the intensity of a headache in patients before and after drug treatment. The data consist of before and after intensities for each patient. A) Dependent samples B) Independent samples 4 15) Answer Key Testname: CHAPTER 9 PRACTICE 1) H0 : p1 = p2 . H1 : p1 p2 . Test statistic: z = 0.97. Critical values: z = ±1.96. Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that the recognition rates are the same in both states. H1 : p1 < p2 . 2) H0 : p1 = p2 . Test statistic: z = -2.41. Critical value: z = -1.28. Reject the null hypothesis. There is sufficient evidence to support the claim that p1 < p2 . 3) H0 : p1 = p2 . H1 : p1 p2 . Test statistic: z = 1.93. Critical values: z = ±1.96. Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that the two proportions are equal. H1 : p1 > p2 . 4) H0 : p1 = p2 . Test statistic: z = 1.21. Critical value: z = 1.645. Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that the proportion of women favoring stricter gun control is higher than the proportion of men favoring stricter gun control. H1 : p1 p2 . 5) H0 : p1 = p2 . Test statistic: z = 3.19. Critical values: z = ±2.575. Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that the proportion of smokers in the two age groups is the same. H1 : p1 < p2 . 6) H0 : p1 = p2 . Test statistic: z = -1.80. Critical value: z = -2.05. Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that the vaccine is effective in lowering the incidence of the disease. 7) D A 9) A 8) 10) H0 : µ1 = µ2 . H1 : µ1 µ2 . Test statistic t = 16.025. Critical values: t = ±2.032. Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean. 11) H0 : µ1 = µ2 H1 : µ1 µ2 Test statistic: t = -1.506 0.1 < P-value < 0.2 Do not reject H . At the 10% significance level, there is not sufficient evidence to support the claim that the mean 0 GPA of students at college A is different from the mean GPA of students at college B. 12) H0 : µ1 = µ2 . H1 : µ1 < µ2 . Test statistic: t = -1.477. Critical value: -2.473. Do not reject the null hypothesis. There is not sufficient evidence to support the claim that the treatment group is from a population with a smaller mean than the control group. 5 Answer Key Testname: CHAPTER 9 PRACTICE 13) H0 : µ1 = µ2 H1 : µ1 < µ2 Test statistic: t = -0.795 Critical value: t = -1.701 Do not reject H0 . At the 5% significance level, there is not sufficient evidence to support the claim that the mean amount of time spent watching television by women is smaller than the mean amount of time spent watching television by men. 14) H0 : µ1 = µ2 H1 : µ1 > µ2 Test statistic: t = 1.274 Critical value: t = 2.060 Do not reject H0 . At the 2.5% significance level, there is not sufficient evidence to support the claim that the mean resting pulse rate of people who do not exercise regularly is larger than the mean resting pulse rate of people who exercise regularly. 15) A 6