Practice Problems for Final Exam The final exam will be Multiple Choice and T/F only. 1. Tourism is a major source of income for many Caribbean countries. Suppose the Bureau of Tourism for Barbados estimates from a sample of 500 tourists that the average amount spent per day by a tourist is $110 with a margin of error of $2 at a 90% confidence level. Which of the following statements is consistent with this information? A. A 95% confidence level would increase the margin of error. B. An 80% confidence level would increase the margin of error. C. A smaller sample would have resulted in a smaller margin of error. D. A larger sample would have resulted in a smaller sample average. 2. An article in your local newspaper claims that the average time to sell a home in your area is 60 days. You take a sample of 20 homes sold recently and find a 95% confidence interval to be 65 ± 3 days. Your correct conclusion is that: A. Your sample indicates that all homes take longer than 60 days to sell. B. Your sample must have been taken incorrectly. C. You don’t see any inconsistency between your confidence interval and the statement in the newspaper. D. The newspaper article must be incorrect. Your confidence interval indicates that the average time to sell a home is greater than 60 days. 3. The nicotine content in cigarettes of a certain brand is normally distributed, with mean (in milligrams) and standard deviation = 0.1. The brand advertises that the mean nicotine content of its cigarettes is 1.6, but you are suspicious and plan to investigate the advertised claim by testing the hypotheses Ho: = 1.6 vs. Ha: > 1.6. You have calculated the critical value of EMBED Equation.3 to be 1.64. The power of this test when the true value of is 1.8 is: A. P( EMBED Equation.3 <1.64 | = 1.8). B. P( EMBED Equation.3 <1.64 | = 1.6). C. P( EMBED Equation.3 >1.64 | = 1.8). D. P( EMBED Equation.3 >1.64 | = 1.6). 4. When testing the difference in two treatment responses one could apply each treatment to the same group of individuals and compare the individual treatment results by calculating the individual differences. This type of testing procedure is called a A. Two sample test. B. One sample test. C. Matched pairs design. D. Two tailed test. 5. A New York real estate firm tracks the cost of apartment rentals in the US. In mid-2002, the nationwide mean apartment rental rate was $895 per month (The Wall Street Journal, July 8, 2002). Have apartment rates increased since then? A current sample from 2004 resulted in a z score of 1.12. Based on this, you would conclude that A. Yes, the sample provides strong evidence to conclude that apartment rates have increased since 2002. B. No, the sample does not provide evidence that apartment rates have changed since 2002. C. The P – value is approximately 0.1314. D. Both B and C. 6. The expected value of the sample mean, EMBED Equation.3 , is the same as the mean () of the population. A. True. B. False. 7. In general, the variance of a sampling distribution is dependent on the sample size but not the population size. A. True. B. False. 8. A magazine states the following hypotheses about the average age of their subscribers: Ho: = 28 years vs. Ha: > 28 years. Making a Type I error with this test means that A. The sample result gives little evidence to conclude that the average age of the subscribers is greater than 28 years when in fact the average age IS 28 years. B. The sample result gives little evidence to conclude that the average age of the subscribers is greater than 28 years when in fact the average age is much greater than 28 years. C. The sample result gives strong evidence that the average age is greater than 28 years when in fact the average age IS 28 years. D. The sample result gives strong evidence that the average age is greater than 28 years when in fact the average age is much greater than 28 years. 9. Suppose we want a 95% confidence interval for the amount spent on books by freshmen in their first year at a major university. The interval is to have a margin of error of $3, and the amount spent has a normal distribution with a standard deviation = $30. The number of observations needed is closest to: A. 609. B. 20. C. 385. D. 271. 10. In the latest presidential election, 55% of the citizens of Lancaster county voted for George W. Bush. A researcher is interested in finding out if the percentage of voters in Lancaster county who agree with how President Bush has handled the economy is different than the percentage that voted for him. Let represent the proportion of voters who agree with how President Bush has handled the economy. Which of the following hypotheses should the researcher test? A. Ho: = 0.55 vs. Ha: < 0.55. B. Ho: = 0.55 vs. Ha: ≠ 0.55. C. Ho: = 0.55 vs. Ha: > 0.55. D. Ho: = 0.55 vs. Ha: < 0.45. 12. A production manager is considering switching to a new assembly method for one of his products. He has reason to believe that the new method will result in an increase in the production rate. Currently they produce an average of 2000 items each week. He has tested the new method for the past 4 weeks and found that the sample average is 2145 with sample standard deviation, s = 76. In order to justify switching to the new method the manager will test the hypotheses: Ho: = 2000 vs. Ha: > 2000. The P – value associated with this sample result is: A. between 0.05 and 0.025. B. between 0.025 and 0.01. C. 3.82. D. Less than 0.001. 13. The Leeds School of Business is considering doing away with their introductory computer course for freshmen and allowing students to take an online instructional program to learn Excel. To compare the effectiveness of the online program, two samples of freshmen were used. One sample of 15 students took the freshman introductory course, the second sample of 20 students used the online program. Each sample of freshmen was then asked to complete a set of tasks on Excel. The time required to complete the tasks was recorded for each student. Assume that the population variances are not equal. Suppose that the calculated t statistic for this data is 1.45. Assuming a one-tailed test the P – value would be: A. 0.0735. B. Between 0.10 and 0.05. C. Between 0.20 and 0.10. D. Impossible to determine given the degrees of freedom are undefined. 14. The t procedures are considered robust when referring to the assumption of a normal population distribution. This means that slight departures from normality will still result is reliable tests results, provided of course that the sample data come from a random sample. A. True. B. False. Use the following information to answer questions 15 - 17: A local ice cream shop sponsored a free ice cream giveaway in order to promote their new flavor, Gingerbread. The ice cream shop believes that the new flavor will be profitable if the majority of their customers like the new flavor well enough to purchase it next time. To determine whether they should add this flavor the shop used the following hypotheses. Ho: = 0.5 vs. Ha: > 0.5 A random sample of customers was asked if they would buy the new flavor. Out of 60 customers, 35 said they would buy it next time they visited. 15. Find the z statistic associated with this sample. A. -1.29. B. 1.29. C. 1.31. D. -1.31. 16. Suppose the P – value is 0.0823. Are the results of this test significant at the 0.05 significance level? A. Yes. B. No. 17. Regardless of your answer to 16, assume that the sample result is not significant. Which of the following conclusions makes sense? A. The ice cream shop should stop offering Gingerbread ice cream. B. The ice cream shop should add Gingerbread ice cream to their selection. 18. A TV special said there is a 10 percent incidence of sexually transmitted disease (STD) among all U.S. teens. A reporter for the Rockville Bugle, looking for a story, surveyed 260 randomly chosen teenagers, and found that 39 had been to a clinic for STD treatment. The p-value for this right sided test is: A) .0036 B) 2.69 C) .0119 D) 2.26 19. Which of the following statements is correct? A) When testing the mean of individual differences one uses matched pairs of data. B) When testing the difference between two population means, one uses data that come from independent samples. C) When testing the difference betweent two population means using independent samples, one must make an assumption about the equality of population variances. D) All of the above. 20. Larger samples of paired quantitative variables always result in stronger correlations between the variables A) True B) False Use the following to answer questions 21-23: A new policy of “flex hours” is proposed. Random sampling showed that 28 of 50 female workers favored the change, while 22 of 50 male workers favored the change. Management wonders if there is a difference between the two groups. 21. The value of the pooled proportion is A) .44 B) .50 C) .56 D) none of the above 22. Given that the calculated z statistic is 1.2, the p-value for this two-sided test would be A) .1151 B) .2302 C) .5000 D) .3849 23. Based on your p-value, you would conclude A) In 23% of the cases, men and women differ in the proportion that favor the flex time policy. B) there is not enough evidence to conclude that men and women differ in the proportion that favor the flex time policy. C) the evidence clearly suggests that men and women differ in the proportion that favor the flex time policy. D) the results are inconclusive. Use the following to answer questions 24 and 25: The Jolly Blue Giant Health Insurance Company guideline says that average hospitalization for a triple hernia operation should not exceed 3 days. The auditor is suspicious that the average stay is actually greater than three days. 24. Set up the null and alternative hypotheses used to test her suspicion. A) H0: = 3 vs. H1: = 5 B) H0: = 3 vs. H1: EMBED Unknown 3 C) H0: = 3 vs. H1: < 3 D) H0: = 3 vs. H1: > 3 25. The diligent auditor studied records of 16 randomly chosen triple hernia operations at HackMore Hospital, and found a mean hospital stay of 4 days with a standard deviation of 2 days. The p-value is A) .0456 B) .025 < p-value < .05 C) .05 < p-value < .1 D) .0228 26. Variability in a process is always unpredictable. A) True B) False 27. The median is not resistant to outliers. A) True B) False 28. Making predictions from a regression model by extrapolation is not a good idea. A) True B) False 29. Correlation coefficients should be calculated for quantitative variables only. A) True B) False 30. A financial institution wishes to estimate the mean balances owed by its credit card customers. The population standard deviation is estimated to be $300. If a 99 percent confidence interval is used and an interval of $75 is desired, how many cardholders should be sampled? A) 87 B) 107 C) 629 D) 3382 31. Variability in a sampling distribution is related to sample size, not population size. A) True B) False 32. In hypothesis testing, Type I error is A) the probability of rejecting H0 when H1 is true. B) always equal to 5 percent. C) always smaller or equal to 5 percent. D) the probability of rejecting H0 when H0 is true. Use the following to answer questions 33-36: SUMMARY OUTPUT Regression Statistics Multiple R 0.97163127 R Square 0.94406733 Adjusted R Square 0.93976482 Standard Error 123.411013 Observations 15 ANOVA df SS MS F Significance F Regression 1 3341863 3341863 219.4223 1.61E-09 Residual 13 197993.6 15230.28 Total 14 3539856 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 173.463643 86.69624 2.000821 0.066742 -13.8322 360.7595 Size 0.31330964 0.021151 14.81291 1.61E-09 0.267615 0.359004 33. The value of the correlation coefficient for Assessed Value and Floor Space is A) .313 B) .944 C) .567 D) .972 34. Predict the Assessed Value of a property that has 1400 square feet of floor space. A) $177,380 B) $611.20 C) $611,200 D) $177.38 35. The equation of the regression line for Assessed Value and Floor Space is A) EMBED Unknown B) EMBED Unknown C) EMBED Unknown D) EMBED Unknown 36. The percentage of variation in Assessed Value explained by Floor Space is A) 3% B) 97% C) 30% D) 94% 39. Given the following sample data, calculate the standard error for the two sample t test statistic assuming the population variances are not equal. n1 = 42, s1 = 13, n2 = 35, s2 = 21. A) 4.077 B) .954 C) .664 D) 16.624 Use the following to answer questions 40-42: 40. This hypothesis test is A) a right-tailed test. B) a two-tailed test. C) a left-tailed test. D) None of the above. 41. Suppose the alternate value of we are concerned about is .0095 and the critical value of the sample proportion, p, is .0097 Which of the following statements describes power? A) P( p > .0097 | = .0098) B) P( p < .0097 | = .0095) C) P( p > .0097 | = .0095) D) P( p < .0097 | = .0098) 42. Based on the reported p-value and = 0.05 one should A) reject the null hypothesis. B) neither reject nor fail to reject the null hypothesis C) take several more samples to see if your conclusions are the same each time. D) fail to reject the null hypothesis. 43. A poll showed that 48 out of 120 randomly chosen graduates of California medical schools last year intended to specialize in family practice. What is the width of a 90% confidence interval for the proportion that plan to specialize in family practice? A) .07357 B) ± .08765 C) .08944 D) .04472 44. The exponential distribution describes a continuous random variable. A) True B) False 45. You should never use a t statistic for testing a hypothesis about a proportion. A) True B) False 46. The owner of Limp Pines Resort wanted to know the average age of its clients. A random sample of 25 tourists is taken. It shows a sample mean age of 46 years with a sample standard deviation of 5 years. The width of a 98 percent CI for the true mean client age is approximately A) 2.33 years. B) 2.79 years. C) 2.06 years. D) 2.49 years. 47. Which of the following is correct? A) The level of significance refers to the probability of making a Type II error. B) A Type I error can never occur if you reject H0. C) When your sample size increases, the probability of a Type II error will decrease and the probability of a Type I error will stay the same. D) A Type II error can never occur if you fail to reject H0. 48. For a given sample size, the higher the confidence level the A) smaller the interval width. B) more accurate the answer. C) greater the interval width. D) smaller the error. 49. You will always reject the null hypothesis when the p-value is less than . A) True B) False 50. The slope in a regression model tells you the strength of the linear relationship between the two variables. A) True B) False These problems will help you with calculations. 1. An engineer designs an improved light bulb. The previous design had an average lifetime of 1500 hours. The mean lifetime of a random sample of 20 new bulbs is found to be 1510 hours. The P-value for this sample result was 0.3458 and the results of this sample are not statistically significant. If, in fact, there is a difference between the mean lifetimes of the two light bulbs, what type of error has the researcher committed? 2.. Haverty’s Furniture is a family business that has been selling to retail customers in the Chicago area for many years. They advertise extensively on radio, TV, and the Internet, emphasizing their low prices and easy credit terms. The owner would like to review the relationship between sales and the amount spent on advertising. The table below gives sales and advertising expense for the last four months. Use Excel Month Ad Expense ($ million) Sales Revenue ($ million) July 3 8 August 1 3 September 2 5 October 5 10 November 6 11 a. Find the correlation coefficient for these two variables. b. Find the equation of the regression line. c. Find the coefficient of determination. d. What percentage of variation in Sales Revenue is explained by Ad Expense? 3. The Leeds School of Business is looking at the relationship between FCQ course summary data and other course variables. One variable of interest is the average grade earned by the students in a course. The table below shows frequency data for the two variables for over 1000 courses taught in the last several years. We would like to perform a Chi Square test of independence between these two variables. FCQ Course Rating Course GPA A B C D A 250 75 45 12 B 120 150 80 50 C 25 58 100 68 D 0 35 30 50 State the null and alternative hypotheses to be tested. Calculate the Chi Square term for FCQ Course Rating B and Course GPA C. It turns out that the p-value for this test statistic is approximately zero. State your conclusion regarding your hypotheses in part a. 4. The western regional sales manager for a textbook publishing company would like to estimate the average number of sales calls that her sales reps make in their territory each week. To investigate, she takes a random sample of 28 sale reps for the past week and finds that the sample mean number of calls is 42 and the sample standard deviation, s, is 5.1 calls. Find the 95% confidence interval for the mean number of calls made each week. Assume the distribution on number of sales calls is approximately normal. 5. A production manager is considering switching to a new assembly method for one of his products. He has reason to believe that the new method will result in an increase in the production rate. Currently they produce an average of 2000 items each week. He has tested the new method for the past 4 weeks and found that the sample average is 2145 with sample standard deviation, s = 76. In order to justify switching to the new method the manager will test the hypotheses: Ho: = 2000 vs. Ha: > 2000. The P – value associated with this sample result is: 6. Slot machines are the favorite game at casinos throughout the US. Suppose we would like to test the hypothesis that there is no difference between the proportion of women that say slots is the favorite game and the proportion of men that say slots is their favorite game. The following sample data show the number of women and number of men who selected slot machines as their favorite game. Women Men Sample Size, n 320 250 Favorite Game – Slots 230 135 The z score calculated from this sample data is 7. The Leeds School of Business is considering doing away with their introductory computer course for freshmen and allowing students to take an online instructional program to learn Excel. To compare the effectiveness of the online program, two samples of freshmen were used. One sample of 20 students took the freshman introductory course, the second sample of 25 students used the online program. Each sample of freshmen was then asked to complete a set of tasks on Excel. The time required to complete the tasks was recorded for each student. Assume that the population variances are not equal. Suppose that the calculated t statistic for this data is 1.45. Assuming a one-tailed test the P – value would be: 8. The Miller Department store age study provides the following data on the ages of customers from independent random samples taken at their two store locations. We would like to test the hypothesis that there is no difference in average customer age between the two stores. Calculate the t statistic used for this test. Assume the population variances are not equal. Inner-city Store Urban Store n1 = 36 n2 = 49 EMBED Equation.3 = 40 years EMBED Equation.3 = 35 years s1 = 9 years s2 = 10 years 9. The cost of transportation from the airport to the downtown area depends on the method of transportation. One-way costs for taxi and shuttle bus transportation for a sample of 10 major cities shows that the sample mean of the difference in costs for each city is EMBED Equation.3 = $9.35 and the sample standard deviation of the differences is sD = $2.95. Find the margin of error for a 95% confidence interval. 10. Microsoft Outlook is the most widely used e-mail manager. A Microsoft executive claims that Microsoft Outlook is used by at least 75% of Internet users. The null and alternative hypotheses used to test this claim are Ho: = 0.75 vs. Ha: ≠ 0.75 A sample of 300 Internet users showed that 246 use Microsoft Outlook. Find the P – value associated with this sample. . Answers to Practice Final Questions A D C C D A A C C B No number 11 B B A B B A A D B B B B D B B B A A B A D D B C D A A A C B A A A A D C C A B Short Answer: Type II a. .9755 b. y=2.023+1.581x c. .9516 d. 95.16% a. Null: Variables independent, Alternative: Variables dependent b. 1.912 c. Reject the null. 42 +/- 1.978 done in earlier problem z = 4.413 done in earlier problem t = 2.414 2.11 .0052 PAGE 1