STAT CH. 9 (FOR ARMODRILLO1)

Chapter 9

Question 1 A bond analyst is analyzing the interest rates for equivalent municipal bonds issued by two different states. At α = 0.05 , is there enough evidence to conclude that there is a difference in the interest rates paid by the two states?

State A State B

Sample size 60 70

Mean interest rate (%) 3.6 3.5

Population variance 0.03 0.03 a. Yes, because the test value 3.28 is outside the critical region −1.96 < z < 1.96

b. No, because the test value 1.08 is inside the critical region −1.96 < z < 1.96

c. Yes, because the test value 10.77 is outside the critical region −1.96 < z < 1.96

d. No, because the test value 0.01 is inside the critical region −1.96 < z < 1.96

Question 2 In October, the campus bookstore asked a random set of freshmen and seniors how much they had spent on textbooks that semester. The bookstore believes that the two groups spent the same amount. What is an appropriate test value for a z test?

Freshmen Seniors

Sample size 60 40

Sample mean $280 $290

Population std. dev. $47 $58 a. –0.08 b. 11.00 c. –0.91 d. –1.23

Question 3 A sociologist wants to determine if the life expectancy of people in Africa is less than the life expectancy of people in Asia. The data obtained is shown in the table below.

Africa Asia X̄1=63.63 yr. X̄2=65.2 yr. σ 1=9.1 yr. σ2=7.3 yr. n1=120 n2=150

Calculate the critical value. Use α = 0.05 . a. –1.65 b. –2.33 c. –2.58 d. –1.96

Question 4 A sociologist expects the life expectancy of people in Africa is different than the life expectancy of people in Asia. The data obtained is shown in the table below. Determine the 95% confidence interval for the difference in the population means.

Africa Asia X̄1=55.3 yr. X̄2=65.2 yr. σ 1=8.1 yr. σ2=9.3 yr. n1=53 n2=42

a. . −12.2 < μ1 − μ2 < −6.9 b. −13.5 < μ1 − μ2 < −6.3 c. −11.4 < μ1 − μ2 < −7.6 d. −16.3 < μ1 − μ2 < −6.0

Question 5 A pharmaceutical company is testing the effectiveness of a new drug for lowering cholesterol. As part of this trial, they wish to determine whether there is a difference between the effectiveness for women and men. At α = 0.05 , what is an appropriate test value?

Women Men

Sample size 60 50

Mean effectiveness 4.4 3.9

Population variance 3.6 3.6 a. 3.79 b. 0.36 c. 0.73 d.1.38

Question 6 A marketing firm asked a random set of married and single men how much they were willing to spend on a vacation. Is there sufficient evidence at α = 0.05 to conclude that is there a difference in the two amounts?

Married men Single men

Sample size 50 40

Sample mean $640 $665

Population variance 5700 9100 a. No, because the test value –0.07 is inside the critical region −1.96 < z < 1.96 .

b. No, because the test value –1.35 is inside the critical region −1.96 < z < 1.96 .

c. No, because the test value –1.60 is inside the critical region −1.96 < z < 1.96 .

d. No, because the test value –1.60 is outside the critical region −1.96 < z < 1.96 .

Question 7 Mauricio Cruz, a wine merchant for Cruz's Spirits Emporium, wants to determine if the average price of imported wine is less than the average price of domestic wine. He obtained the data shown in the table below.

Imported wine Domestic wine X̄1=$7.03 X̄2=$9.78 s1=$2.31 s2=$3.62 n=15 n=16

What is the critical value at α = 0.05 ? a. –1.761 b.-1.753 c. –2.145 d. –2.131

Question 8 Mauricio Cruz, a wine merchant for Cruz's Spirits Emporium, wants to determine if the average price of imported wine is less than the average price of domestic wine. He obtained the data shown in the table below.

Imported wine Domestic wine X̄1=$7.03 X̄2=$9.78 s1=$2.31 s2=$3.62 n=15 n=16

What is the appropriate test value for a t test? a. –6.49 b. –4.46 c. –2.54 d. –0.92

Question 9 In a test of the difference between the two means below, what should the test value be for a t test?

Sample 1 Sample 2

Sample mean 80 95

Sample variance 600 80

Sample size 8 11 a. –0.07 b. –0.13 c. –0.18 d. –1.65

Question 10 A marketing firm asked a random set of married women and married men how much they were willing to spend for jewelry as a present for their spouse.

Can the firm conclude, at α = 0.05 , that the two groups have a different willingness to spend?

Women Men

Sample size 10 11

Sample mean $80 $115

Sample standard deviation $34 $28 a. No, because the test value –0.19 is inside the noncritical region −2.228 < t <2.228

b. Yes, because the test value –2.56 is outside the noncritical region −2.262 < t <2.262

c. Yes, because the test value –0.82 is inside the noncritical region −2.228 < t <2.228

d. No, because the test value –0.82 is outside the noncritical region −2.262 < t <2.262

Question 11 A reporter bought hamburgers at randomly selected stores of two different restaurant chains, and had the number of Calories in each hamburger measured. Can the reporter conclude, at α = 0.05 , that the hamburgers from the two chains have a different number of Calories?

Chain A Chain B

Sample size 5 9

Sample mean 280 Cal 335 Cal

Sample standard deviation 19 Cal 27 Cal a. No, because the test value –0.36 is inside the noncritical region −2.306 < t <2.306

b. Yes, because the test value –0.36 is inside the noncritical region −2.776 < t <2.776

c. Yes, because the test value –4.44 is outside the noncritical region −2.776 < t <2.776

d. No, because the test value –1.42 is inside the noncritical region −2.306 < t <2.306

Question 12 A medical researcher is interested in whether patients' left arms or right arms are longer. If 10 patients participate in this study, how many degrees of freedom should the researcher use when finding the critical value for a t test? a. 9 b. 10 c. 18 d. 19

Question 13 A poll found that 38% of male voters and 46% of female voters support a particular candidate. To test whether this candidate has equal levels of support between male and female voters, the null hypothesis should be a. . H0 :pmale=pfemale b. . H0 :pmale=50%,H0: pfemale=50% c. . H0 :pmale=38%,H0: pfemale=46% d. H0 :pmale<pfemale .

Question 14 Find p̄ and q̄ , if X1=17, n1=20, X2=28, andn2=60 a. p̄=0.56, q̄=0.44 b. p̄=0.66, q̄=0.34 c. p̄=0.34, q̄=0.66 d. p̄=0.44, q̄=0.56

Question 15 A recent survey reported that in a sample of 300 students who attend two-year colleges, 105 work at least 20 hours per week. Additionally, in a sample of 225 students attending private four-year universities, only 20 students work at least 20 hours per week. What is the test value for a test of the difference between these two population proportions? a. 6.95 b. 7.61 c. 2.38 d. 4.18

Question 16 66% of students at a university live on campus. A random sample found that 25 of 40 male students and 46 of 60 of female students live on campus. At the 0.05 level of significance, is there sufficient evidence to support the claim that a difference exists between the proportions of male and female students who live on campus? a. Yes, because the test value –16.51 is outside the noncritical region −1.96 < z < 1.96

b. No, because the test value –0.76 is inside the noncritical region −1.96 < z < 1.96 .

c. Yes, because the test value –3.37 is outside the noncritical region −1.96 < z < 1.96

d. No, because the test value –1.53 is inside the noncritical region −1.96 < z < 1.96 .

Question 17 Many elementary school students in a school district currently have ear infections. A random sample of children in two different schools found that 16 of 44 at one school and 18 of 40 at the other have ear infections. At the 0.05 level of significance, is there sufficient evidence to support the claim that a difference exists between the proportions of students who have ear infections at the two schools?

a. Yes, because the test value –7.51 is outside the noncritical region −1.96 < z < 1.96 .

b. No, because the test value –0.81 is inside the noncritical region −1.96 < z < 1.96 .

c. No, because the test value –1.06 is inside the noncritical region −1.96 < z < 1.96

d. Yes, because the test value –4.16 is outside the noncritical region −1.96 < z < 1.96

Question 18 A study of cats and dogs found that 34 of 55 cats and 19 of 50 dogs slept more than 10 hours per day. At the 0.05 level of significance, is there sufficient evidence to conclude that a difference exists between the proportions of cats and dogs that sleep more than 10 hours per day? a. Yes, because the test value 2.44 is outside the noncritical region −1.96 < z < 1.96 .

b. Yes, because the test value 2.79 is outside the noncritical region −1.65 < z < 1.65

c. Yes, because the test value 6.34 is outside the noncritical region −1.65 < z < 1.65 .

d. Yes, because the test value 7.80 is outside the noncritical region −1.96 < z < 1.96

Question 19 What is the critical value for a two-tailed F test with α = 0.10 , when the sample size from which the variance for the numerator was obtained is 10, and the sample size from which the denominator was obtained is 24? a. 2.27 b. 2.25 c. 2.32 d. 2.30

Question 20 For the samples summarized below, test the hypothesis, at α = 0.05 , that the two variances are different.

Sample 1 Sample 2

Sample Std. Deviation 4.4 2.7

Sample size 10 20 a. Reject the hypothesis because the test value 2.66 is less than the critical value 2.88. b. Reject the hypothesis because the test value 2.66 is less than the critical value 2.35. c. Accept the hypothesis because the test value 7.05 is greater than the critical value 2.77.

d. Reject the hypothesis because the test value 7.05 is greater than the critical value 2.42.

Question 21 In comparing the two standard deviations below, what test value and degrees of freedom should be used in an F test?

Sample 1 Sample 2

Standard deviation 5 4

Sample size 17 25 a. test value = 1.25; d.f.N. = 17 and d.f.D. = 25 b. test value = 1.25; d.f.N. = 24 and d.f.D. = 16 c. test value = 1.56; d.f.N. = 25 and d.f.D. = 17 d. test value = 1.56; d.f.N. = 16 and d.f.D. = 24

Question 22 A car salesman claims that the variance of prices on convertibles is higher than the variance of prices on station wagons. The standard deviation of the list price on 16 convertibles is $6800 and the standard deviation on 24 station wagons is $3900. What should the test value be? a. 1.74 b. 3.04 c. 2.25 d. 1.53

Question 23 Given the variances of the two samples below, find the test value and the degrees of freedom that should be used in an F test.

Sample 1 Sample 2

Variance 7 13

Sample size 11 29 a. test value = 3.45; d.f.N. = 29 and d.f.D. = 11 b. test value = 0.54; d.f.N. = 28 and d.f.D. = 10 c. test value = 1.86; d.f.N. = 28 and d.f.D. = 10 d. test value = 1.36; d.f.N. = 29 and d.f.D. = 11

Question 24 A researcher hypothesized that the variation in the car rental rates (in US$/day) at a major city airport is less than in the car rental rates down town. A survey found that the variance of the rental rates on 8 cars at the airport was 35.7 while the variance of the rental rates on 5 cars down town was 50.4. What test value should be used in a F test? a. 2.26 b. 1.19 c. 1.41 d. 1.99

Question 25 For the samples summarized below, test the hypothesis that the two variances are equal, at α = 0.05

Sample 1 Sample 2

Sample variance 25 10

Sample size 8 18 a. Accept the hypothesis because the test value 6.25 is greater than the critical v value 3.16. b .Reject the hypothesis because the test value 2.50 is less than the critical value 3.01. c. Reject the hypothesis because the test value 6.25 is greater than the critical value 3.01. d. Accept the hypothesis because the test value 2.50 is less than the critical value 3.16.