# Math 210 - Exam 5 - Sample Exam

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Math 210 - Exam 5 - Sample Exam

Math 210 - Exam 5 - Sample Exam 1) A researcher claims that the responses occur with percentages of 15%, 20%, 25%, 25%, and 15% respectively. Below is a sample of responses. If the claim is true, how many times would you expect the response to be "D"? Response A B C D E Frequency 12 15 16 18 19 A) 4.5 B) 6.1 C) 22.3 D) 20 2) A random sample of 4 homes in Dutchess County, New York is taken. The selling price and the list price of each home is taken. Use the data to obtain a 90% confidence interval for the mean difference, µd , in the selling price and list price of homes in Dutchess County. Home Selling Price List Price A $377,500 $385,000 B $268,000 $275,000 A) -7815 < µd < -3885 C) -8508 < µd < -3192 C $379,000 $383,900 D $225,000 $229,000 B) -10728 < µd < -971.9 D) -9642 < µd < -2058 3) Ten different families are tested for the number of gallons of water a day they use before and after viewing a conservation video. Let the differences be D = Before - After. Determine the alternative hypothesis to test the claim that water usage has decreased. Before 33 33 38 33 35 35 40 40 40 31 After 34 28 25 28 35 33 31 28 35 33 A) H1: µd < 0 B) H1: µd > 0 C) H1: µd 0 D) H1: µd 0 4) Find the correlation coefficient, r. x 23.6 35.3 18.3 49.0 13.2 y 4 9 3 3 8 A) -0.178 B) 0 C) -0.2 1 D) 0.2 5) A random sample of cars is taken. The color of the car and whether it was in an accident was also recorded. Find the critical value needed to test the claim that the row and column variable ard independent at the 0.01 significance level. Red Blue White Car has been in accident Car has not been in accident A) 9.210 28 33 36 23 22 30 B) 4.605 C) 16.812 D) 10.645 6) 155 students who were majoring in either math or English were asked a test question, and the researcher recorded whether they answered the question correctly. The sample results are given below. If the row and column variables are independent, how many in the sample would you expect to be math majors and answer the question correctly? Correct Incorrect Math 22 53 English 43 37 A) 31.45 B) 30.77 C) 29.31 D) 32.14 7) 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 H1: µd > 0 at the 0.1 level of significance. What is the p-value? A) 1.415 B) 3.036 C) 0.0095 2 D) 2.326 8) A random sample of oceanfront (directly on the beach) and oceanside homes in Long Beach Island are taken. Use the information below to find the p-value for testing the claim that the mean price of oceanfront homes is greater than the mean price of oceanside homes (H1: µOF > µOS). Sample Means Sample SDs Sample Sizes A) 0.0124 Oceanfront Oceanside $2,574,200 $1,036,800 762,561.93 $39995.25 5 5 B) 0.0038 C) 0.0053 D) 0.0275 9) A researcher wishes to determine whether the blood pressure of vegetarians is lower than the blood pressure of nonvegetarians. Independent simple random samples of 85 vegetarians and 75 nonvegetarians yielded the following sample statistics for systolic blood pressure. Find the test statistic needed to test the claim. Vegetarians n1 = 85 Nonvegetarians n2 = 75 x1 = 124.1 mmHg s1 = 38.7 mmHg A) -2.365 x2 = 138.7 mmHg s2 = 39.2 mmHg B) 0.0096 C) -2.589 D) 0.0057 10) Determine the slope of the least square regression line. x 1 3 5 7 9 y 143 116 100 98 90 A) 140.4 B) -6.2 C) 150.7 3 D) 6.8 11) The table below shows the age and favorite type of music of 668 randomly selected people. Determine the test statistic needed to test the claim that age and music preference are independent. Rock Pop Classical 15-25 50 85 73 25-35 68 91 60 35-45 90 74 77 A) 12.954 B) 16.919 C) 9.488 D) 11.143 12) You roll a die 48 times with the following results. Number 1 2 3 4 5 6 Frequency 13 3 12 15 2 3 Find the test statistic to test the claim that the die is fair. A) 14.13 B) 7.092 C) 8 D) 22 13) 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 C) -0.0443 < p1 - p2 < 0.0976 B) -0.0034 < p1 - p2 < 0.0566 D) 0.0247 < p1 - p2 < 0.0286 14) In studying the occurrence of genetic characteristics, the following sample data were obtained. Find the critical value needed to test the claim that the characteristics occur with the same frequency at the 0.05 significance level. Characteristic A B C D E F Frequency 28 30 45 48 38 39 A) 12.592 B) 8.263 C) 16.750 D) 11.071 ^ 15) Ten pairs of data yield the regression equation y = 2.08 + 3.29x. What is the predicted value of y for x = 2? A) 17.0 B) 8.66 C) 8.0 4 D) 7.0 16) Find the equation of the least squares regression line. x 1.2 1.4 1.6 1.8 2.0 y 54 53 55 54 56 ^ B) y = 50.4 + 2.50x ^ ^ D) y = 54 A) y = 50 + 3x ^ C) y = 55.3 + 2.40x 17) From a sample of 5000 American Airlines passengers, 22 had their luggage lost. From a sample of 4000 Delta Airlines passengers, 15 were lost. What is the test statistic for testing the claim that the proportion of luggage lost is the same for both airlines (H1: pAA pDA)? A) 0.4037 B) 0.632 C) 0.5119 D) 0.4788 18) A researcher was interested in comparing the GPAs of students at two different colleges. Independent simple random samples of 8 students from college A and 13 students from college B yielded the following GPAs. Determine the alternative hypothesis to test the claim that the mean GPA is higher for College B. College A College B 3.7 3.8 3.2 3.2 3.0 3.0 2.5 3.9 2.7 3.8 3.6 2.5 2.8 3.9 3.4 A) H1: µA > µB 2.8 4.0 3.6 2.6 4.0 3.6 B) H1: µA < µB C) H1: µA µB D) H1: µA µB 19) It is claimed that the proportion of gloves that leak virus is greater for vinyl (V) gloves than latex (L) gloves. What is H1 for testing this claim? A) H1: pV pL B) H1: pV < pL 5 C) H1: pV > pL D) H1: pV pL 20) 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. At the 0.05 significance level, find the p-value to test the claim that the recognition rates are the same in both states. A) 0.333 B) 0.968 C) 0.459 D) 0.013 21) A paint manufacturer wished to compare the drying times of two different types of paint. Independent simple random samples of 11 cans of type A and 9 cans of type B were selected and applied to similar surfaces. The drying times, in hours, were recorded. The summary statistics are as follows. Construct a 98% confidence interval for µ1 - µ2, the difference between the mean drying time for paint of type A and the mean drying time for paint of type B. Type A Type B x1 = 77.5 hrs x2 = 63.6 hrs s1 = 4.5 hrs s2 = 5.1 hrs n1 = 11 n2 = 9 A) 8.35 hrs < µ1 - µ2 < 19.45 hrs C) 8.42 hrs < µ1 - µ2 < 19.38 hrs B) 8.58 hrs < µ1 - µ2 < 19.22 hrs D) 8.28 hrs < µ1 - µ2 < 19.52 hrs 22) We wish to test a hypothesis about paired data. Suppose that d = 3.345, Sd = 1.984, and n = 12, and that you wish to test H1: µd > 0. Determine the critical value needed to test the hypothesis at the 0.01 level of significance. A) 3.106 B) 2.718 C) 2.576 D) 2.326 \ 23) 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. What is the test statistic needed to test the claim that the additive increases the yield? Plot: 1 Before 9 After 10 A) -1.584 2 9 9 3 8 9 4 7 8 5 6 7 6 8 10 7 5 6 B) -2.033 8 9 10 9 10 10 C) -5.014 6 10 11 12 D) -2.536 24) If d = 3.125, Sd = 2.911, and n = 8, determine a 95 percent confidence interval for µd. A) 2.264 < µd < 5.559 B) 0.691 < µd < 5.559 C) 0.691 < µd < 3.986 D) 2.264 < µd < 3.986 25) Suppose you wish to test the claim that µ d, the mean value of the differences d for a population of paired data, is less than 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 H0 if the test statistic is less than -1.717. B) Reject H0 if the test statistic is less than 1.717. C) Reject H0 if the test statistic is less than -1.714. D) Reject H0 if the test statistic is less than 1.714. 7