HW 7 Solutions

Section 7.1

Page 312, #16

H_o: m = 24 (claim)

H_a: m ≠ 24

Page 313, #20

H_o: p = .02

H_a: p ≠ .02

Type I Error: Rejecting the null hypothesis p=.02 when p is .02.

Type II Error: Not rejecting the null hypothesis p=.02 when p really is not .02.

Page 313, #26

H_o: m ≥ 50,000

H_a: m < 50,000

This is a left-tailed test.

Page 313, #34

H_o: m = 26 calories

H_a: m ≠ 26 calories

(a) There is enough evidence to reject the soft drink maker’s claim.

(b) There is not enough evidence to reject the soft drink maker’s claim.

Page 314, #38

(a) H_o: m ≤ 28

H_a: m > 28

As the internet provider, you want to support the claim that the mean time spent on line is more than 28 minutes, so this needs to be in the alternative hypothesis. To support a claim, you put it in the alternative hypothesis, hoping that you have enough evidence to reject the null hypothesis.

(b) H_o: m ≥ 28

H_a: m < 28

As the advertiser, you want to reject the claim that the mean time is more than 28 minutes.

Section 7.2

Page 326, #22

(a) H_o: m = 80 (claim)

H_a: m ≠ 80

Given: n = 42, , s = 35, a = .05

(b) z₀ = 1.96 Rejection region: z > 1.96, z < -1.96

(c)

(d) Since z < z_o, fail to reject H₀. There is not enough evidence to reject the claim by the coffee shop that the mean caffeine content is 80 mg per 5 ounces.

Page 326, #24

Given: , n = 52, a = .04, s = 10

(a) H_o: m ≤ 230 (claim)

H_a: m > 230

(b) z₀ = 1.75 Rejection region: z > 1.75

(c)

(d) z < 1.75 Fail to reject H₀. There is not enough evidence to refute the

claim that the sodium content per cereal serving is no more than 230 mg.

Page 327, #32

Given: , n = 60, s = 1.13

(a) H_o: m = 3.4 (claim)

H_a: m ≠ 3.4

(b)

(c) p-value = 2(.0853) = .1706 [Note this is a two-sided test]

(d) a = .80

Reject H₀, since p < a. There is enough evidence to reject the hypothesis that the mean consumption of tuna by Americans is 3.4 pounds per year, at the a = .80 level.

Section 7.3

Page 337, #18

(a) H_o: m ≤ 95

H_a: m > 95 (claim)

(b) t₀ = 3.143 Rejection region: reject H₀ if t > t₀.

(c)

(d) Fail to reject the H₀. There is not enough evidence to support the claim that mean repair cost is greater than $95.

Page 337, #20

(a) H_o: m ≤ 4

H_a: m > 4 (claim)

(b) t₀ = 1.833

Rejection region: reject H₀ if t > t₀.

(c)

(d) t < t₀, so fail to reject H₀. There is not enough evidence to support the claim that the mean waste generated by American adults is more than 4 pounds per day.

Section 7.4

Page 344, #10

(a) H_o: p ≤ .50

H_a: p > .50 (claim)

(b) z₀ = 1.282

Rejection region: reject H₀ if z > 1.282

(c)

(d) Fail to reject H₀. There is not enough evidence to support the claim that more than 50% of British consumers want supermarkets to stop selling genetically modified food.

Page 345, #12

(a) H_o: p = .70 (claim)

H_a: p ≠ .70

(b) z₀ = 1.96 Rejection region: reject H₀ if z < -1.96 or if z > 1.96.

(c)

(d) Reject H₀. There is enough evidence to reject the claim that 70% of Americans believe the government is inefficient and wasteful.

Section 7.5

Page 354, #18

(a) H₀: s² = 5 (claim)

H_a: s² ≠ 5

(b) , since there are 22 degrees of freedom and a = .05.

Rejection region: reject H0 if c² > 36.781 or if c² < 10.982.

(c)

(d) Fail to reject H₀. There is not enough evidence to reject the claim that the variance for gas mileage for luxury sedans is 5 miles per gallon.

Page 354, #20

(a) s ≥ 30

s < 30 (claim)

(b) , since a = .01 and there are 9 degrees of freedom.

Rejection region: reject H₀ if c² < 2.088.

(c)

(d) Fail to reject H₀. There is not enough evidence to support the claim that the standard deviation of test scores for 8^th graders who took the life science assessment test was less than 30.