ECO 045 - Practice Problems for Final Exam - Part2 Fall 2019 PDF

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Warning: TT: undefined function: 32Lehigh UniversityECO 045Practice Problems for Final Exam – Part 2Yuval ErezFall 2019 In interval estimation, as the sample size becomes larger, the interval estimate a. becomes narrower. b. becomes wider. c. remains the same, because the mean is not changing. d. ge...

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Lehigh University ECO 045 Practice Problems for Final Exam – Part2

Yuval Erez Fall 2019

1. In interval estimation, as the sample size becomes larger, the interval estimate a. becomes narrower. b. becomes wider. c. remains the same, because the mean is not changing. d. gets closer to 1.96. ANSWER: a

2. When s is used to estimate σ, the margin of error is computed by using the a. normal distribution. b. t distribution. c. mean of the sample. d. mean of the population. ANSWER: b

3. From a population with a variance of 900, a sample of 225 items is selected. At 95% confidence, the margin of error is a. 15. b. 2.0. c. 3.92. d. 4. ANSWER: c

4. In interval estimation, the t distribution is applicable only when a. the population has a mean of less than 30. b. the sample standard deviation is used to estimate the population standard deviation. c. the variance of the population is known. d. the mean of the population is unknown. ANSWER: b

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5. From a population that is not normally distributed and whose standard deviation is not known, a sample of 6 items is selected to develop an interval estimate for the mean of the population (μ). a. The normal distribution can be used. b. The t distribution with 5 degrees of freedom must be used. c. The t distribution with 6 degrees of freedom must be used. d. The sample size must be increased. ANSWER: d

6. From a population that is normally distributed, a sample of 25 elements is selected and the standard deviation of the sample is computed. For the interval estimation of μ, the proper distribution to use is the a. normal distribution. b. t distribution with 25 degrees of freedom. c. t distribution with 26 degrees of freedom. d. t distribution with 24 degrees of freedom. ANSWER: d

7. As the sample size increases, the margin of error a. increases. b. decreases. c. stays the same. d. fluctuates depending on the mean. ANSWER: b

8. A 95% confidence interval for a population mean is determined to be 100 to 120. For the same data, if the confidence coefficient is reduced to .90, the confidence interval for μ a. becomes narrower. b. becomes wider. c. does not change. d. becomes 100.1 to 120.1. ANSWER: a

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9. In general, higher confidence levels provide a. wider confidence intervals. b. narrower confidence intervals. c. a smaller standard error. d. unbiased estimates. ANSWER: a

10. A sample of 225 elements from a population with a standard deviation of 75 is selected. The sample mean is 180. The 95% confidence interval for μ is a. 105 to 225. b. 175 to 185. c. 171.78 to 188.22. d. 170.2 to 189.8. ANSWER: d

11. A random sample of 64 students at a university showed an average age of 25 years and a sample standard deviation of 2 years. The 98% confidence interval for the true average age of all students in the university is (Hint: You need to use the t-table here, since the population standard deviation is unknown) a. 20.5 to 29.5. b. 24.4 to 25.6. c. 23.0 to 27.0. d. 20.0 to 30.0. ANSWER: b

12. The sample size needed to provide a margin of error of 2 or less with a .95 probability when the population standard deviation equals 11 is a. 10. b. 11. c. 116. d. 117. ANSWER: d

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13. It is known that the population variance equals 484. With a .95 probability, the sample size that needs to be taken if the desired margin of error is 5 or less is a. 190. b. 74. c. 189. d. 75. ANSWER: d

14. The following random sample from a population whose values were normally distributed was collected. 10

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The 95% confidence interval for μ is a. 8.52 to 11.48. b. 7.75 to 12.25. c. 9.25 to 10.75. d. 8.00 to 10.00. ANSWER: b

15. The following random sample from a population whose values were normally distributed was collected. 10

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The 80% confidence interval for μ is a. 12.054 to 15.946. b. 10.108 to 17.892. c. 10.321 to 17.679. d. 11.009 to 16.991. ANSWER: d

16. In a random sample of 100 observations, 𝑃" = .2. The 95.44% confidence interval for p is a. .122 to .278. b. .164 to .236. c. .134 to .266. d. .120 to .280. ANSWER: d

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17. A random sample of 1000 people was taken. Four hundred fifty of the people in the sample favored Candidate A. The 95% confidence interval for the true proportion of people who favor Candidate A is a. .419 to .481. b. .40 to .50. c. .45 to .55. d. .424 to .476. ANSWER: a

18. A machine that produces a major part for an airplane engine is monitored closely. In the past, 10% of the parts produced would be defective. With a .95 probability, the sample size that needs to be taken if the desired margin of error is .04 or less is a. 110. b. 111. c. 216. d. 217. ANSWER: d

19. We are interested in conducting a study to determine the percentage of voters of a state would vote for the incumbent governor. What is the minimum sample size needed to estimate the population proportion with a margin of error of .05 or less at 95% confidence? (Hint: with the lack of any information, assume that p* = 0.5). a. 200. b. 100. c. 58. d. 385. ANSWER: d

20. A random sample of 64 SAT scores of students applying for merit scholarships showed an average of 1400 with a (sample!) standard deviation of 240. The 95% confidence interval for the population mean SAT score is a. 1340.06 to 1459.94. b. 1341.20 to 1458.80. c. 1349.93 to 1450.07. d. 1320.32 to 1479.68. ANSWER: a

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21. A sample of 75 information systems managers had an average hourly income of $40.75 with a standard deviation of $7.00. The value of the margin of error at 95% confidence is a. 80.83. b. 7.00. c. .81. d. 1.61. ANSWER: d

22. We can use the normal distribution to make confidence interval estimates for the population proportion, p, when a. np > 5. b. n(1 - p) > 5. c. p has a normal distribution. d. both np > 5 and n(1 - p) > 5. ANSWER: d

23. To compute the necessary sample size for an interval estimate of a population proportion, all of the following procedures are recommended when p is unknown except a. use the sample proportion from a previous study. b. use the sample proportion from a preliminary sample. c. use 1.0 as an estimate. d. use judgment or a best guess. ANSWER: c

24. The degrees of freedom associated with a t distribution are a function of the a. area in the upper tail. b. sample standard deviation. c. confidence coefficient. d. sample size. ANSWER: d

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25. The margin of error in an interval estimate of the population mean is a function of all of the following except a. α. b. sample mean. c. sample size. d. variability of the population. ANSWER: b

26. A local university administers a comprehensive examination to the candidates for B.S. degrees in Business Administration. Five examinations are selected at random and scored. The scores are shown below. Scores 80 90 91 62 77 a. b. c.

Compute the mean and the standard deviation of the sample. Compute the margin of error at 95% confidence. Assume the population is normally distributed. Develop a 95% confidence interval estimate for the mean of the population.

ANSWER: a. Mean = 80, s = 11.77 (rounded). b. 14.61 c. 65.39 to 94.61

27. Many people who bought X-Game gaming systems over the holidays have complained that the systems they purchased were defective. In a sample of 1200 units sold, 18 units were defective. a. b.

Determine a 95% confidence interval for the percentage of defective systems in the population. If 1.5 million X-Game gaming systems were sold over the holidays, determine an interval for the number of defectives in sales.

ANSWER:

a. .00812 to .02188 (rounded) b. 12,184 to 32,816 (using unrounded estimates)

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28. Two hundred students are enrolled in an Economics class. After the first examination, a random sample of 6 papers was selected. The scores were 65, 75, 89, 71, 70, and 80. a. b. c.

Determine the standard error of the mean. What assumption must be made before we can determine an interval for the mean score of all the students in the class? Explain why. Assume the assumption of Part b is met. Provide a 95% confidence interval for the mean score of all the students in the class.

ANSWER:

a.

3.474 Since n is small and σ is estimated from s, we must assume the distribution of all the b. scores is normal. c. 66.07 to 83.93 (rounded)

29. What type of error occurs if you fail to reject H0 when, in fact, it is not true? a. Type II b. Type I c. either Type I or Type II, depending on the level of significance d. either Type I or Type II, depending on whether the test is one-tailed or two-tailed ANSWER: a

30. For a given sample size in hypothesis testing, a. the smaller the Type I error, the smaller the Type II error will be. b. the smaller the Type I error, the larger the Type II error will be. c. Type II error will not be effected by Type I error. d. the sum of Type I and Type II errors must equal to 1. ANSWER: b

31. In hypothesis testing, the tentative assumption about the population parameter is a. the alternative hypothesis. b. the null hypothesis. c. either the null or the alternative. d. neither the null nor the alternative. ANSWER: b

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32. The p-value is a. the same as the z statistic. b. a sample statistic. c. a distance. d. a probability. ANSWER: d

33. For a lower (one) tail test, the p-value is the probability of obtaining a value for the test statistic a. at least as small as that provided by the sample. b. at least as large as that provided by the sample. c. at least as small as that provided by the population. d. at least as large as that provided by the population. ANSWER: a

34. The level of significance is the a. maximum allowable probability of Type II error. b. maximum allowable probability of Type I error. c. same as the confidence coefficient. d. same as the p-value. ANSWER: b

35. Which of the following does not need to be known in order to compute the p-value? a. knowledge of whether the test is one-tailed or two-tailed b. the value of the test statistic c. the level of significance d. the probability distribution of the test statistic ANSWER: c

36. As the test statistic becomes larger, the p-value a. gets smaller. b. becomes larger. c. goes beyond 1. d. becomes negative. ANSWER: a

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37. For a lower tail test, the test statistic z is determined to be zero. The p-value for this test is a. zero. b. -.5. c. +.5. d. 1. ANSWER: c

38. The average manufacturing work week in metropolitan Chattanooga was 40.1 hours last year. It is believed that the recession has led to a reduction in the average work week. To test the validity of this belief, the hypotheses are a. H0: μ < 40.1 Ha: μ ≥ 40.1. b. H0: μ ≥ 40.1 c. H0: μ > 40.1

Ha: μ < 40.1.

d. H0: μ = 40.1

Ha: μ ≠ 40.1.

Ha: μ ≤ 40.1.

ANSWER: b

39. A sample of 1400 items had 280 defective items. For the following hypothesis test, H0: p ≤ .20

Ha: p > .20

the test statistic is a. .28. b. .14. c. .20. d. zero. ANSWER: d

40. A random sample of 16 students selected from the student body of a large university had an average age of 25 years and a standard deviation of 2 years. We want to determine if the average age of all the students at the university is significantly more than 24. Assume the distribution of the population of ages is normal. The test statistic is a. 1.96. b. 2.00. c. 1.65. d. .05. ANSWER: b

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41. A random sample of 16 students selected from the student body of a large university had an average age of 25 years and a standard deviation of 2 years. We want to determine if the average age of all the students at the university is significantly more than 24. Assume the distribution of the population of ages is normal. Using α = .05, it can be concluded that the population mean age is a. not significantly different from 24. b. significantly different from 24. c. significantly less than 24. d. significantly more than 24. ANSWER: d

42. A grocery store has an average sales of $8000 per day. The store introduced several advertising campaigns in order to increase sales. To determine whether or not the advertising campaigns have been effective in increasing sales, a sample of 64 days of sales was selected. It was found that the average was $8300 per day. From past information, it is known that the standard deviation of the population is $1200. The p-value is a. 2.000. b. .9772. c. .0228. d. .5475. ANSWER: c

43. The average price of homes sold in the U.S. in 2012 was $240,000. A sample of 144 homes sold in Chattanooga in 2012 showed an average price of $246,000. It is known that the standard deviation of the population (σ) is $36,000. We are interested in determining whether or not the average price of homes sold in Chattanooga is significantly more than the national average. a. b. c. d.

State the null and alternative hypotheses to be tested. Compute the test statistic. The null hypothesis is to be tested at the 5% level of significance. Determine the critical value(s) for this test. What do you conclude?

ANSWER: a.

H0: μ ≤ $240,000 Ha: μ > $240,000 b. Test statistic z = 2 c. z.05 = 1.645 d. Reject H0 and conclude that the average price in Chattanooga is higher than the national average.

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44. The average U.S. daily internet use at home is two hours and twenty minutes. A sample of 64 homes in Soddy-Daisy showed an average usage of two hours and 50 minutes with a standard deviation of 80 minutes. We are interested in determining whether or not the average usage in Soddy-Daisy is significantly different from the U.S. average. a. b. c. d.

State the null and alternative hypotheses to be tested. Compute the test statistic. The null hypothesis is to be tested using α = .05. Determine the critical value(s) for this test. What do you conclude?

ANSWER: a.

H0: μ = 140 minutes Ha: μ ≠ 140 minutes b. Test statistic t = 3 c. t.025 = 1.998 and -t.025 = -1.998 d. Reject H0 and conclude that the average usage in Soddy-Daisy is significantly different from the national average of 140 minutes.

45. In 2012, seventy percent of Canadian households had an internet connection. A sample of 484 households taken in 2013 showed that 75% of them had an internet connection. We are interested in determining whether or not there has been a significant increase in the percentage of the Canadian households that have internet connections. a. b. c. d.

State the null and alternative hypotheses to be tested. Compute the test statistic. The null hypothesis is to be tested at the 5% level of significance. Determine the critical value(s) for this test. What do you conclude?

ANSWER: a.

H0: p ≤ .70 Ha: p > .70 b. Test statistic z = 2.4 (rounded) c. z.05 = 1.645 d. Reject H0 and conclude that there has been a significant increase.

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46. A tire manufacturer has been producing tires with an average life expectancy of 26,000 miles. Now the company is advertising that its new tires' life expectancy has increased. In order to test the legitimacy of the advertising campaign, an independent testing agency tested a sample of 6 of their tires and has provided the following data. Life Expectancy (In Thousands of Miles) 28 27 25 28 29 25 a. b.

Determine the mean and the standard deviation. At the .01 level of significance using the critical value approach, test to determine whether or not the tire company is using legitimate advertising. Assume the population is normally distributed.

ANSWER: a. = 27, s = 1.67 (rounded) b. H0: μ < 26 (in thousands of miles) Ha: μ > 26 (in thousands of miles) Since t = 1.467 < 3.365, do not reject H0 and conclude that there is insufficient evidence to support the manufacturer's claim.

47. A producer of various kinds of batteries has been producing "D" size batteries with a life expectancy of 87 hours. Due to an improved production process, management believes that there has been an increase in the life expectancy of their "D" size batteries. A sample of 36 batteries showed an average life of 88.5 hours. It is known that the standard deviation of the population is 9 hours. a. b. c. d. e.

Give the null and the alternative hypotheses. Compute the test statistic. At the 1% level of significance using the critical value approach, test management's belief. What is the p-value associated with the sample results? What is your conclusion based on the p-value using α = .01? What is your conclusion based on the p-value using α = .05?

ANSWER: a.

H0: μ < 87 hours Ha: μ > 87 hours b. 1.00 c. Since z = 1 < 2.33, do not reject H0 d. p-value = .1587 > .01; therefore, do not reject H0 and conclude that there is insufficient evidence to support the management's belief. e. p-value = .1587 > .05; therefore, do not reject H0; no evidence to support the management's belief using the 5% level of significance.

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48. Identify the null and alternative hypotheses for the following problems. a. b. c.

The manager of a restaurant believes that it takes a customer less than or equal to 25 minutes to eat lunch. Economists have stated that the marginal propensity to consume is at least 90¢ out of every dollar. It has been stated that 75 out of every 100 people who go to the movies on Saturday night buy popcorn.

ANSWER: a.

H0: μ < 25 Ha: μ > 25 b. H0: p > .9 Ha: p < .9 c. H0: p = .75 Ha: p ≠ .75

49. A sample of 64 account balances from a credit company showed an average daily balance of $1040. The standard deviation of the population is known to be $200. We are interested in determining if the mean of all account balances (i.e., population mean) is significantly different from $1000. a. b. c. d. e.

Develop the appropriate hypotheses for this problem. Compute the test statistic. Compute the p-value. Using the p-value approach and α = .05, test the above hypotheses. What is your conclusion? Using the critical value approach and α = .05, test the hypotheses. What is your conclusion?

ANSWER: a.

H0: μ = $1000 Ha: μ ≠ $1000 b. 1.60 c. .1096 d. p-value = .1096 > α = .05. The null hypothesis is not rejected; no evidence to show that the mean is significantly different from $1000. e. z = 1.60 is between -1.96 and 1.96; the null hypothesis cannot be rejected; there is no evidence that the mean is significantly different from $1000.

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50. UHON Research Group has tested the hypotheses regarding the IQ of university honor students. They provided the following information. H0: µ ≤ 144 Ha: µ > 144 (Genius) Sample size n = 121 Sample mean = 145 p-value = .0054 a. b.

Using α = .015, would you reject or not reject the null hypothesis? Explain how you arrived at your answer and what you can conclude about the IQ scores of UHON students? The researchers failed to report the standard deviation. Determine the standard deviation. Use the normal distribution table to answer this question and show your complete work.

ANSWER: a. b.

Reject H0 because p-value = .0054 < α = .015. It can be concluded that the population mean IQ score of UHON students is more than 144. p-value = .0054 results in test statistic value = 2.55 Solving 2.55 =

gives s = 4.314 (rounded)

51. The standard error of is the a. pooled estimator of - . b. variance of the sampling distribution of

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c. standard deviation of the sampling distribution of d. margin of error of

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