MATH 10 SAMPLE FINAL EXAM. Answers are on the last page at the bottom

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1 MATH 10 SAMPLE FINAL EXAM Answers are on the last page at the bottom I. USE THE INFORMATION BELOW TO ANSWER PROBLEMS 1 THROUGH 3. Among 100 marriage license applications, chosen at random in 1971, there were 8 in which the women were at least one year older than the men, and among 30 marriage license applications, chosen at random in 1977, there were 6 in which the women were at least one year older than the men. Assume you are interested in a 80% confidence interval for the difference between the corresponding true proportions of marriage license applications in which the women were at least one year older than the men. 1. Choose the best answer below concerning a confidence interval for the difference between the corresponding true proportions of marriage license applications in which the women were at least one year older than the men.! s $ a) x ± z " # n % & ˆp ˆq b) ˆp ± z n c) (x 1 x 2 ) ± z 2 2 s 1 n 1 + s 2 n 2 d) ( ˆp 1 ˆp 2 ) ± z ˆp 1 ˆq 1 n 1 + ˆp 2 ˆq 2 n 2 e) None of the above formulas are appropriate. 2. Choose from the following concerning the z-value or t-value that would be used in the 80% confidence interval for the difference between the corresponding true proportions of marriage license applications in which the women were at least one year older than the men. a) z = b) t = c) z = d) t = If we assign group 1 to be the sample from 1971 and group 2 to be the sample from 1977, you may assume that the appropriate confidence interval for the above problem to be (-1.572, ). Based on this interval choose the most appropriate portion below from the conclusion for the confidence interval. a) We are 80% confident that there is no difference between the corresponding true proportions of marriage license applications in which the women were at least one year older than the men. b) We are 80% confident that the true proportion of marriage licenses in which the women were at least one year older than the men was greater in 1971 than in c) We are 80% confident that the true proportion of marriage licenses in which the women were at least one year older than the men was greater in 1977 than in d) Can t answer this question based on the information given. e) None of the above conclusions are correct. 1

2 II. USE THE INFORMATION BELOW TO ANSWER PROBLEMS 4 THROUGH 6. In a study of heart surgery, one issue was the effect of drugs called beta-blockers on the pulse rate of patients during surgery. The available subjects were divided at random into two groups of 21 patients each. One group received a beta-blocker; the other a placebo. The surgical team recorded the pulse rate of each patient at a critical point during the operation. The treatment group had mean 65.2 beats per minute. For the control group, the mean was Below is Minitab output for the beta-blocker data. Assume equal population variances and assume the populations are independent and normally distributed. TWOSAMPLE CI FOR TREATMNT VS CONTROL N MEAN TREATMNT CONTROL PCT CI FOR MU TREATMNT - MU CONTROL: (-1.3, 5.47) 4. Choose the best interpretation below for the confidence interval in the Minitab output. a) We are 95% confident that the true mean number of beats per minute during surgery for patients that receive a beta-blocker is greater than the true mean number of beats per minute during surgery for patients that do not receive a beta-blocker. b) We are 95% confident that there is no statistically significant difference between the true mean beats per minute during surgery for the two groups. c) We are 95% confident that the true mean number of beats per minute during surgery for patients that receive a beta-blocker is less than the true mean number of beats per minute during surgery for patients that do not receive a beta-blocker. d) Can t answer this question based on the information given. e) None of the above conclusions are correct. 5. Pick the formula used to calculate the confidence interval above.! s $ a) x ± z 2 # 1 " # n % & b) (x 1 x 2 ) ± t α s p + 1 & $ % n 1 n 2 ' ( c) (x 1 x 2 ) ± z 2 2 s 1 n 1 + s 2 n 2 d) ( ˆp 1 ˆp 2 ) ± z ˆp 1ˆq 1 n 1 + ˆp 2 ˆq 2 n 2 e) None of the above formulas are appropriate. 6. Pick the appropriate z or t value used in the above interval. a) b) c) d) e) None of the above values are correct. 2

3 III. USE THE INFORMATION BELOW TO ANSWER PROBLEMS 7 THROUGH 11. A researcher wants to test whether the proportion of Foothill students who transfer to a four-year university is different than the proportion of DeAnza students who transfer to a four-year university. 7. Pick the most appropriate answer below concerning the formulation of the null and alternative hypotheses to determine whether the data provide sufficient evidence to conclude that the proportion of Foothill students who transfer to a four-year university is different than the proportion of DeAnza students who transfer to a four-year university. a) H o : µ 1 µ 2 = 0 H A : µ 1 µ 2 0 b) H o : µ 1 µ 2 = 0 H A : µ 1 µ 2 < 0 c) H o : p 1 p 2 = 0 H A : p 1 p 2 0 d) Can t answer the question 8. If the test statistic for the test is z * =1.48, what would be the p-value for the test? a) b) c) d) Can t answer this question. 9. If the test statistic for the test is z * =1.48, then, at the 5% significance level, what would be your conclusion for the test? a) There is suffient evidence to conclude H A is true. b) There is insuffient evidence to conclude H A is true. c) None of the above are correct. 10. Choose the most appropriate portion below from the conclusion for the hypothesis test. a) At the 5% significance level, there is sufficient evidence to conclude that the true proportion of Foothill students who transfer to a four-year university is different than the true proportion of DeAnza students who transfer to a four-year university. b) At the 5% significance level, there is insufficient evidence to conclude that the true proportion of Foothill students who transfer to a four-year university is different than the true proportion of DeAnza students who transfer to a four-year university. c) None of the above are correct. 11. Pick the most appropriate equation that should be used to calculate the test statistic for the test. (You may assume that a z-value is appropriate). a) z * = ˆ p 1 ˆ p 2 " 1 p ˆ q ˆ $ + 1 % ' # n 1 n 2 & b) z * = x 1 x 2 s n 1 + s 2 n 2 c) z * = p ˆ 1 p ˆ 2 " $ ˆ p 1ˆ q 1 p + ˆ 2 q ˆ 2 % ' # & n 1 n 2 d) z * = x 1 x 2 2 " 1 s $ p + 1 % ' # n 1 n 2 & 3

4 IV. USE THE INFORMATION BELOW TO ANSWER PROBLEMS 12 THRU 15. A major car manufacturer wants to test a new engine to see whether it meets new air pollution standards. The emission of all engines of this type must be less than 20 parts per million(ppm) of carbon. 21 engines are manufactured for testing purposes, and the mean and standard deviation of the emissions for this sample of engines are determined to be ppm and 9.49 ppm, respectively. You are interested in whether the data supply sufficient evidence to allow the manufacturer to conclude that this type of engine meets the pollution standard at a 10% level of significance. Below is the appropriate Minitab output for the problem. Assume a normal distribution. N MEAN STDEV SE MEAN T P VALUE CARBON Pick the most appropriate answer below concerning the formulation of the null and alternative hypotheses to determine whether this type of engine meets the pollution standard. a) H o :p = 20 H A :p < 20 b) H o : µ = 20 H A : µ > 20 c) H o : µ = 20 H A : µ < 20 d) H o :p = 20 H A :p > What is the smallest significance level that would allow us to conclude HA is true? a) b) 0.10 c) 0.06 d) Choose the most appropriate portion below from the conclusion for the hypothesis test in problem twelve. a) At the 10% significance level, there is sufficient evidence to conclude that this type of engine meets the pollution standard. b) At the 10% significance level, there is insufficient evidence to conclude that this type of engine meets the pollution standard. c) Not enough information is given to make a conclusion. d) None of the above are correct. 15. Pick the most appropriate equation that should be used to calculate the test statistic for the test in problem twelve. a) z * = x µ o s n b) z * = ˆ p p o p o q o n c) t * = x µ o s n d) t * p = ˆ p o p o q o n 4

5 V. USE THE INFORMATION BELOW TO ANSWER PROBLEMS 16 THRU 18. Suppose you record how long it takes you to get to school over many months and discover that the one-way travel times, in minutes, are approximately normally distributed with a mean of minutes and standard deviation of 4 minutes. If your first class is at 10:30 am, what is the latest time you should leave everyday so that you are on time at least 93.7% of the time? 16. Pick the equation most appropriate to answer the question above. b) p(x) = ( ncx) p x 1 p a) z = x µ σ ( ) n x c) x = µ + zσ d) z = x µ σ n 17. Select the most appropriate item that pertains to the problem a) z = b) z = c) z = d) z = e) None of these. 18. If your first class is at 10:30 am, what is the latest time you should leave everyday so that you are on time at least 93.7% of the time? a) 10:22 am b) 10:00 am c) 10:10 am d) 10:20 am e) None of these. VI. USE THE INFORMATION BELOW TO ANSWER PROBLEMS 19 THRU 21. Based on data from the Statistical Abstract of the United States, the probability that a newborn baby will be a boy is roughly In the next three births, you are interested in the probability that at least two are girls. 19. Pick the equation most appropriate to deal with the problem above. b) p(x) = ( ncx) p x 1 p a) z = x µ σ ( ) n x c) x = µ + zσ d) z = x µ σ n 20. Select the most appropriate item that pertains to the problem a) z = b) z = c) z = d) z = e) None of these. 21. In the next three births, what is the probability that at least two are girls? a) b) c) d) e) None of these. 5

6 VII. USE THE INFORMATION BELOW TO ANSWER PROBLEMS 22 THROUGH 25. With the recent growth in the number of U.S. households wired for cable television, major advertisers are now beginning to show an increased interest in cable advertising. Since its inception, cable television has offered advertisers relatively inexpensive rates and selective target audiences. For purposes of comparison, A.J. Bush and J.H. Leigh conducted a content analysis of television commercials on the three major networks, ABC, CBS, and NBC, and three of the more popular, wellestablished cable networks, CNN, ESPN, and TBS. One of the variables measured was the number of advertisements shown during prime-time (7:00-10:00 P.M.) and late-night (10:00 P.M. - 12:00 A.M.) viewing segments on two weekday evenings during November The results are summarized in the table below. Number of advertisements Prime-time Late-night TOTALS MAJOR ABC NETWORKS CBS NBC CABLE TBS NETWORKS CNN ESPN TOTALS Suppose an advertisement is selected at random from advertisements shown on the two weekday evenings during November What is the probability that the advertisement selected 22. was shown during a late-night segment? a) 163/399 b) 518/917 c) 69/399 d) 399/ was shown on TBS during a prime-time segment? a) 518/917 b) 66/917 c) 113/518 d) 113/ was not shown on a cable network? a) 400/917 b) 517/917 c) 113/917 d) 163/ was shown on ABC during a late-night segment, given that it was shown on a major network? a) 69/917 b) 69/399 c) 69/517 d) 69/163 6

7 VIII. USE THE INFORMATION BELOW TO ANSWER PROBLEMS 26 THROUGH 28. Electric power plants that use water for cooling their condensers sometimes discharge heated water into rivers, lakes, or oceans. It is known that water heated above certain temperatures has a detrimental effect on the plant and animal life in the water. Suppose it is known that the increased temperature of the heated water discharged by a certain power plant in any given day has a normal distribution with a mean of 2.8 degrees Celsius and a standard deviation of 0.6 degrees Celsius. Suppose a sample of 35 days was collected. You are interested in the probability that the mean increase in temperature of the discharged water for the sample exceeds 2.6 degrees Celsius. 26. Pick the equation most appropriate to deal with the problem above. b) p(x) = ( ncx) p x 1 p a) z = x µ σ ( ) n x c) x = µ + zσ d) z = x µ σ n 27. Select the most appropriate item that pertains to the problem a) z = b) z = c) z = d) z = e) None of the above are pertinent to the problem. 28. What is the probability that the sample mean increase in temperature of the discharged water for the sample exceeds 2.6 degrees Celsius. a).9951 b).6293 c).9437 d).9756 IX. USE THE INFORMATION BELOW TO ANSWER PROBLEMS 29 AND 30. The Acculturation Rating Scale for Mexican Americans (ARSMA) measures the extent to which Mexican Americans have adopted Anglo/English culture. During the development of ARSMA, the test was given to a group of 27, randomly chosen, Mexican Americans. Their scores (taken from a normal population), from a possible range of 1.00 to 5.00, had a sample mean of 1.67 points and a sample standard deviation of 0.25 points. Because low scores should indicate a Mexican cultural orientation, these results helped to establish the validity of the test. You are interested in a 90% confidence interval for the true mean ARSMA score of Mexican Americans. 29. Choose the best answer below concerning the 90% confidence interval for the true mean ARSMA score of Mexican Americans. ˆp ( 1 ˆp ) n! s $ a) x ± z " # n % & b) x ± t! s $ " # n % & c) ˆp ± z d) Can t answer this question based on the information given. 30. Choose the appropriate interval from below for the 90% confidence interval for the true mean ARSMA score of Mexican Americans. a) (1.576, 1.764) b) (1.588, 1.752) c) (1.591, 1.749) d) Can t answer this question based on the information given. 7

8 X. USE THE INFORMATION BELOW TO ANSWER PROBLEMS 31 THRU 34 Acme Properties, Inc. specializes in custom home sales in the Evergreen Estates. A random sample of nine currently listed custom homes provided information on size and price. The size data are in hundreds of square feet, rounded to the nearest hundred; the price data are in thousands of dollars, rounded to the nearest thousand. Use the output below to answer the following questions: Correlation of SIZE and PRICE = ROW SIZE PRICE MTB > Regress 'PRICE' 1 'SIZE' The regression equation is PRICE = SIZE Predictor Coef Stdev t-ratio p Constant SIZE s = R-sq = 86.4% R-sq(adj) = 84.5% Predict the price of a custom home in the Evergreen Estates that is 29 hundred square feet. a) $269,000 b) $295,000 c) $276,600 d) $558, Predict the price of a custom home in the Evergreen Estates that is 47 hundred square feet. a) $475,000 b) $535,800 c) $817,800 d) $195, State the value of slope of the regression line. a) -141 b) 14.4 c) d) Interpret the correlation coefficient. a) There is a strong negative linear relationship between square footage and sale price. b) There is a strong positive linear relationship between square footage and sale price. c) There is a weak negative linear relationship between square footage and sale price. d) There is a weak positive linear relationship between square footage and sale price. 8

9 Problem 35 is a stand-alone problem and has nothing to do with the previous problem. 35. What can we say about the percentage of data that lies within 2 standard deviations of the mean? a) Approximately 95% b) Approximately 75% c) At least 75% d) At most 25% XI. USE THE INFORMATION BELOW TO ANSWER PROBLEMS 36 and 37 Suppose you record how long it takes you to get to school over many months and discover that the one-way travel times, in minutes, are approximately normally distributed with a mean of minutes and standard deviation of 4 minutes. You are interested in the probability that it will take you at least 20 minutes to get to school 36. Pick the equation most appropriate to deal with the problem above. a) z = x µ σ b) p(x) = ( ncx) p x ( 1 p) n x c) x = µ + zσ d) z = x µ σ n 37. What is the probability that it will take you at least 20 minutes to get to school? Round your final answer to 2 decimal places. a) 0.03 b) 0.06 c) 0.97 d) 0.94 ANSWERS: 1. D 2. C 3. C 4. B 5. B 6. D 7. C 8. B 9. B 10. B 11. A 12. C 13. C 14. A 15. C 16. C 17. A 18. C 19. B 20. E 21. C 22. D 23. B 24. B 25. C 26. D 27. B 28. D 29. B 30. B 31. C 32. E 33. B 34. B 35. C 36. A 37. B Sample Final 9

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