Math 227 (Statistics) Ch9 Practice Test MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

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1 Math 227 (Statistics) Ch9 Practice Test Section 9.2 Find the number of successes x suggested by the given statement. 1) A computer manufacturer randomly selects 2140 of its computers for quality assurance and finds that 2.76% of these computers are found to be defective. A) 57 B) 62 C) 64 D) 59 1) From the sample statistics, find the value of p used to test the hypothesis that the population proportions are equal. 2) n1 = 44 n2 = 490 2) x1 = 17 x2 = 191 A) B) C) D) Compute the test statistic used to test the null hypothesis that p1 = p2. 3) In a vote on the Clean Water bill, 45% of the 205 Democrats voted for the bill while 52% of the 230 Republicans voted for it. A) B) C) D) ) Find the appropriate p-value to test the null hypothesis, H0: p1 = p2, using a significance level of ) n1 = 50 n2 = 75 x1 = 20 x2 = 15 A).0146 B).1201 C).0032 D) ) Use the traditional method to test the given hypothesis. Assume that the samples are independent and that they have been randomly selected 5) A marketing survey involves product recognition in New York and California. Of 558 New 5) 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. 6) In a random sample of 360 women, 65% favored stricter gun control laws. In a random 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 ) 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) x1 = 65, n1 = 90 and x2 = 79, n2 = 116; Construct a 98% confidence interval for the difference between population proportions p1 - p2. A) < p1 - p2 < B) < p1 - p2 < C) < p1 - p2 < D) < p1 - p2 < ) 1

2 8) In a random sample of 300 women, 50% favored stricter gun control legislation. In a random sample of 200 men, 26% favored stricter gun control legislation. Construct a 98% confidence interval for the difference between the population proportions p1 - p2. A) < p1 - p2 < B) < p1 - p2 < C) < p1 - p2 < D) < p1 - p2 < ) Section 9.3 Determine whether the samples are independent or consist of matched pairs. 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) Matched pairs B) Independent samples 10) 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) Independent samples B) Matched pairs 9) 10) Test the indicated claim about the means of two populations. Assume that the two samples are independent and that they have been randomly selected. 11) Two types of flares are tested for their burning times (in minutes) and sample results are 11) given below. Brand X Brand Y n = 35 n = 40 x = 19.4 x = 15.1 s = 1.4 s = 0.8 Refer to the sample data to test the claim that the two populations have equal means. Use a 0.05 significance level. 12) A researcher wishes to determine whether people with high blood pressure can reduce their blood pressure by following a particular diet. Use the sample data below to test the claim that the treatment population mean µ1 is smaller than the control population mean µ2. Test the claim using a significance level of ) Treatment Group Control Group n1 = 85 n2 = 75 x1 = x2 = s1 = 38.7 s2 = 39.2 The two data sets are dependent. Find d to the nearest tenth. 13) A B A) 41.0 B) 19.7 C) 32.8 D) ) 2

3 Find sd. 14) The differences between two sets of dependent data are 3, 21, 3, 27, 15. Round to the nearest tenth. 14) A) 13.9 B) 21.4 C) 10.7 D) 8.6 Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are independent and that they have been randomly selected. 15) Two types of flares are tested for their burning times (in minutes) and sample results are given 15) below. Brand X Brand Y n = 35 n = 40 x = 19.4 x = 15.1 s = 1.4 s = 0.8 Construct a 95% confidence interval for the differences µx - µy based on the sample data. A) 3.2 < µx - µy < 5.4 B) 3.6 < µx - µy < 5.0 C) 3.5 < µx - µy < 5.1 D) 3.8 < µx - µy < 4.8 Assume that you want to test the claim that the paired sample data come from a population for which the mean difference is µd = 0. Compute the value of the t test statistic. 16) x y A) t = B) t = C) t = D) t = ) 17) The following table shows the weights of nine subjects before and after following a particular diet for two months. You wish to test the claim that the diet is effective in helping people lose weight. What is the value of the appropriate test statistic? Subject A B C D E F G H I Before After A) B) C) D) ) Determine the decision criterion for rejecting the null hypothesis in the given hypothesis test; i.e., describe the values of the test statistic that would result in rejection of the null hypothesis. 18) Suppose you wish to test the claim that µd, the mean value of the differences d for a population of 18) paired data, is different from 0. Given a sample of n = 23 and a significance level of = 0.05, what criterion would be used for rejecting the null hypothesis? A) Reject null hypothesis if test statistic > or < B) Reject null hypothesis if test statistic > C) Reject null hypothesis if test statistic > or < D) Reject null hypothesis if test statistic > or < ) Suppose you wish to test the claim that µd, the mean value of the differences d for a population of paired data, is greater than 0. Given a sample of n = 15 and a significance level of = 0.01, what criterion would be used for rejecting the null hypothesis? A) Reject null hypothesis if test statistic > B) Reject null hypothesis if test statistic > or < C) Reject null hypothesis if test statistic > D) Reject null hypothesis if test statistic < ) 3

4 20) A farmer has decided to use a new additive to grow his crops. He divided his farm into 10 plots and kept records of the corn yield (in bushels) before and after using the additive. The results are shown below. Plot: Before After You wish the test the following hypothesis at the 1 percent level of significance. 20) H0: µd = 0 against H1: µd > 0. What decision rule would you use? A) Reject H0 if test statistic is greater than or less than B) Reject H0 if test statistic is greater than C) Reject H0 if test statistic is greater than D) Reject H0 if test statistic is less than ) We wish to compare the means of two populations using paired observations. Suppose that d = 3.125, Sd = 2.911, and n = 8, and that you wish to test the following hypothesis at the 5 percent level of significance: 21) H0: µd = 0 against H1: µd > 0. What decision rule would you use? A) Reject H0 if test statistic is greater than and less than B) Reject H0 if test statistic is greater than C) Reject H0 if test statistic is less than D) Reject H0 if test statistic is greater than Use the traditional method of hypothesis testing to test the given claim about the means of two populations. Assume that two dependent samples have been randomly selected from normally distributed populations. 22) Five students took a math test before and after tutoring. Their scores were as follows. 22) Subject A B C D E Before After Using a 0.01 level of significance, test the claim that the tutoring has an effect on the math scores. 23) A test of abstract reasoning is given to a random sample of students before and after they completed a formal logic course. The results are given below. At the 0.05 significance level, test the claim that the mean score is not affected by the course. Before After ) 4

5 Construct a confidence interval for µd, the mean of the differences d for the population of paired data. Assume that the population of paired differences is normally distributed. 24) Using the sample paired data below, construct a 90% confidence interval for the population mean of all differences x - y. x y A) < µd < 1.77 B) < µd < 1.47 C) 0.22 < µd < 7.48 D) < µd < ) 25) A test of writing ability is given to a random sample of students before and after they completed a formal writing course. The results are given below. Construct a 99% confidence interval for the mean difference between the before and after scores. Before After A) 1.2 < µd < 2.8 B) -0.5 < µd < 4.5 C) -0.2 < µd < 4.2 D) -0.1 < µd < ) 5