Mathematics

Chapter 8 Test

Question 1 Using the z table, find the critical value (or values) for an α = 0.09 two-tailed test. a. 1.34 b. 69 c. 1.34 d. 1.69

Question 2 Using the z table, find the critical value (or values) for an α = 0.11 right-tailed test. a. .61 b. 0.80 c. 1.23 d. 1.60

Question 3 Using the z table, determine the critical values for a two-tailed test when α = 0.03 . a. ± 1.88 b. ± 2.17 c. ± 0.18 d. ± 0.06

Question 4 A recent survey of gasoline prices indicated that the national average was $4.098 per gallon. The Dallas Automobile Club claimed that gasoline in Texas was significantly lower than the national average. A survey covering 10 different suburbs in Dallas found the average price of gasoline to be $3.924 per gallon with a population standard deviation of $0.053. What critical value should be used to test the claim using α = 0.01 ? a. 1.26 b. 2.33 c. –1.26 d. –2.33

Question 5 If the sample mean is 7, the hypothesized population mean is 5, and the population standard deviation is 2, compute the test value needed for the z test. a. 1.00 b. 2.00 c. –2.00 d. –1.00

Question 6 The Eagle Ridge Contractors Association claims the average price of a home in their subdivision is $125,150 with a standard deviation of $7,350. A sample of 36 homes for sale in this subdivision had an average selling price of $123,550. The Eagle Ridge Home Owners Association is interested in knowing if the costs of homes for sale in this subdivision are actually lower than claimed? Compute the test value? a. –1.31 b. 1.31 c. –1.52 d.1.52

Question 7 At a certain university, the average cost of books was $330 per student last semester and the population standard deviation was $75. This semester a sample of 50 students revealed an average cost of books of $365 per student. The Dean of Students believes that the costs are greater this semester. What is the test value for this hypothesis? a. 0.47 b. 0.70 c. 3.30 d. 23.33

Question 8 An average department store sells 350 men’s suits per year. The men’s suit departments at a particular national chain of stores claim they sell more than the industry average. In 35 of their stores, they sold, on the average, 430 suits per year with a population standard deviation of 40. What is the test value for their claim? a. 0.34 b. 2.00 c. 6.92 d. 11.83

Question 9 The average greyhound can reach a top speed of 18.7 meters per second. A particular greyhound breeder claims her dogs are faster than the average greyhound. A sample of 45 of her dogs ran, on average, 19.1 meters per second with a population standard deviation of 1.6 meters per second. With α = 0.05 , is her claim correct?

a. Yes, because the test value 0.04 falls in the noncritical region. b. No, because the test value 0.04 falls in the critical region. c. Yes, because the test value 1.68 falls in the critical region. d. No, because the test value 0.40 falls in the critical region.

Question 10 Nationwide, the average waiting time until a electric utility customer service representative answers a call is 260 seconds. The Gigantic Kilowatt Energy Company randomly sampled 30 calls and found that, on average, they were answered in 227 seconds with a population standard deviation of 40 seconds. Can the company claim that they are faster than the average utility at α = 0.05 ? a. Yes, because the test value –4.52 falls in the critical region. b. No, because the test value –0.83 falls in the critical region. c. Yes, because the test value –0.15 falls in the critical region. d. No, because the test value –0.15 falls in the critical region.

Question 11 An average computer mouse inspector can inspect 60 mice per hour with a population standard deviation of 10 mice per hour. The 48 computer mice inspectors at a particular factory can only inspect 55 mice per hour. Does the company have reason to believe that these inspectors are slower than average at α = 0.10 ?

a. Yes, because the test value –3.46 falls in the noncritical region. b. No, because the test value –1.98 falls in the critical region. c. Yes, because the test value –3.46 falls in the critical region. d. No, because the test value –1.98 falls in the noncritical region.

Question 12 A recent report by the American Medical Association stated the average annual salary of psychiatrists is $189,121 with a population standard deviation of $26,975. A group of hospital administrators randomly sampled 64 psychiatrists and found an average annual salary of $198,630. The group claims that the average annual salary is actually higher than what the American Medical Association reported. What is the p-value for this one-sided test? a. 0.0024 b. 0.0035 c. 0.1328 d. 0.0237

Question 13 What is the critical value for a two-tailed t test when α = 0.02 and d.f. = 18? a. 2.878 b. 2.567 c. 2.552 d. 2.110

Question 14 What is the critical value for a right-tailed t test when α = 0.025 and d.f. = 12? a. 2.179 b. 0.697 c. 0.695 d. 2.201

Question 15 A recent study of business travelers claims they spend an average of $41.00 per day on meals. As a test of this claim, a random sampling of 16 business travelers found they had spent an average of $45.00 per day with a standard deviation of $3.65. What are the critical values for a two-tailed t test of this claim with α = 0.05 ? a. ± 2.120 b. ± 2.131 c. ± 1.753 d. ± 1.746

Question 16 According to Beautiful Bride magazine, the average age of a groom is now 26.2 years. A sample of 16 prospective grooms in Chicago revealed that their average age was 26.6 years with a standard deviation of 5.3 years. What is the test value for a t test of the claim? a. 1.81 b. 0.30 c. 0.59 d. 2.13

Question 17 At a certain university, the average attendance at basketball games has been 3325. Due to the dismal showing of the team this year, the attendance for the first 8 games has averaged only 2965 with a standard deviation of 735. The athletic director claims that the attendance is the same as last year. What is the test value needed to evaluate the claim? a. –1.39 b. –2.65 c. –3.07 d. –3.92 Question 18 Doctors nationally believe that 68% of a certain type of operation are successful. In a particular hospital, 47 of these operations were observed and 37 of them were successful. At α = 0.05 , is this hospital’s success rate different from the national average?

a. No, because the test value 0.93 is in the noncritical region. b. Yes, because the test value 0.93 is in the critical region. c. No, because the test value 1.58 is in the noncritical region. d. Yes, because the test value 1.58 is in the noncritical region.

Question 19 A scientist claims that only 65% of geese in his area fly south for the winter. He tags 75 random geese in the summer and finds that 23 of them do not fly south in the winter. If α = 0.05 , is the scientist’s belief warranted? a. Yes, because the test value 0.79 is in the noncritical region. b. No, because the test value 0.87 is in the critical region. c. Yes, because the test value –0.87 is in the noncritical region. d. No, because the test value –0.79 is in the noncritical region.

Question 20 A statistician claims that the standard deviation of the weights of firemen is less than 25 pounds. A sample of 20 randomly chosen firemen had a standard deviation of their weights of 26.2 pounds. Assume the variable is normally distributed. At α = 0.05 , what is the critical value χ

2 for this test?

a. 31.410 b. 30.144 c. 10.851 d. 10.117

Question 21 A doctor claims that the standard deviation of systolic blood pressure is 12 mmHg. A random sample of 24 patients found a standard deviation of 14 mmHg. Assume the variable is normally distributed. At α = 0.01 , what are the critical χ

2 values?

a. 9.262 and 44.181 b. 13.091 and 35.172 c. 13.848 and 36.415 d. 11.524 and 44.314

Question 22 A lab technician is tested for her consistency by making multiple measurements of the cholesterol level in one blood sample. The target precision is a standard deviation of 1.1 mg/dL or less. If 16 measurements are taken and the standard deviation is 2.1 mg/dL, is there enough evidence to support the claim that her standard deviation is greater than the target, at α = 0.01 ? a. Yes, since the χ

2 test value 54.669 is greater than the critical value 32.000.

b. No, since the χ 2

test value 28.64 is less than the critical value 30.578. c. Yes, since the χ

2 test value 54.669 is greater than the critical value 30.578.

d. No, since the χ 2

test value 28.64 is less than the critical value 32.000.

Question 23 A lumber mill is tested for consistency by measuring the variance of board thickness. The target accuracy is a variance of 0.0035 square inches or less.

If 24 measurements are made and their variance is 0.006 square inches, is there enough evidence to reject the claim that the standard deviation is within the limit at α = 0.01 ? a. No, since the χ

2 test value 39.43 is less than the critical value 41.638.

b. Yes, since the χ 2

test value 8.22 is less than the critical value 41.638. c. No, since the χ

2 test value 39.43 is less than the critical value 42.980.

d. Yes, since the χ 2

test value 8.22 is less than the critical value 42.980.

Question 24 Assume that a 95% confidence interval for the mean is 14.5 < μ < 16.0 . The null hypothesis H0 : μ 15.0 at α = 0.05 would

a. not be rejected because 15.0 is less than 16.0. b. not be rejected because 15.0 is between 14.5 and 16.0. c. be rejected because 15.0 is more than 14.5. d. be rejected because 15.0 is not equal to 15.25.

Question 25 Assume that a 95% confidence interval for the mean is 15.0 < μ < 19.0 . The null hypothesis H0 :μ=13.0 at α = 0.05 would

a. be rejected because 13.0 is less than 15.0. b. not be rejected because 13.0 is less than 19.0. c. not be rejected because 19.0 is more than 15.0. d. be rejected because 13.0 is not equal equal to 17.0.

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