MAT 300 Midterm Exam

Week 9 Assignment

1. Problem 12, page 523 Effectiveness of Smoking Bans The Joint Commission on Accreditation of Healthcare Organizations mandated that hospitals ban smoking by 1994. In a study of the effects of this ban, subjects who smoke were randomly selected from two different populations. Among 843 smoking employees of hospitals with the smoking ban, 56 quit smoking one year after the ban. Among 703 smoking employees from workplaces without a smoking ban, 27 quit smoking a year after the ban (based on data from “Hospital Smoking Bans and Employee Smoking Behavior” by Longo, Brownson, et al., Journal of the American Medical Association, Vol. 275, No. 16). Is there a significant difference between the two proportions at a 0.05 significance level? Is there a significant difference between the two proportions at a 0.01 significance level? Does it appear that the ban had an effect on the smoking quit rate?

H0: p 1= p 2

H0: p 1 p 2 a = 0.05 or 0.01

Critical region (a = 0.05) : |Z| > 1.96 Critical region (a = 0.01) : |Z| > 2.576

x+ y 56 + 27 Under H0 we have that the best estimate for p is pˆ = = . n+ m 843 + 703

pˆ- p ˆ Z =1 2 = 2.43 Test statistic n+ m pˆ(1- p ˆ ) nm

Conclusions: Since 2.43 > 1.96 we reject H0 at a = 0.05 and conclude that the difference is significant. Since 2.43 < 2.576 we fail to reject H0 at a = 0.01 and conclude that the difference is not significant.

The P-value is 0.015 so it appears that the ban had an effect on the smoking quit rate. 2. Problem 6, page 537 Confidence Interval for Effects of Marijuana Use on College Students Refer to the sample data used in Exercise 5 and construct a 98% confidence interval for the difference between the two population means. Does the confidence interval include zero? What does the confidence interval suggest about the equality of the two population means?

98% CI: 1 1 1 1 m1- m 2 =x 1 - x 2 弊 t sp + =53.3 - 51.3 弊 2.356 4.0714 + = ( 0.311, 3.689) n m 65 64

The interval does not contain zero. Since it does not contain zero it suggests that the difference in means is significant (at a = 0.02 ). 3. Problem 6, page 548 Self-Reported and Measured Male Heights As part of the National Health and Nutrition Examination Survey conducted by the Department of Health and Nutrition Services, self-reported heights and measured heights were obtained for males aged 12-16. Listed below are sample results. a. Is there sufficient evidence to support the claim that there is a difference between self-reported heights and measured heights of males aged 12-16? Use a 0.05 significance level. b. n =12 D =- 1 sD = 3.52

H0 :m= 0

H1 :m 0 a = 0.05 df= n -1 = 12 - 1 = 11

Critical region: |T| > 2.201

D - 1 Test statistic T = = = - 0.98 sD n 3.52 12

Conclusion: Since |-0.98| = 0.95 < 2.201 we fail to reject H0 and conclude that the difference is not significant.

c. Construct a 95% confidence interval estimate of the mean difference between reported heights and measured heights. Interpret the resulting confidence interval, and comment on the implications of whether the confidence interval limits contain 0.

95% CI: s 3.52 m=D� t D - �1 - 2.201( 3.24, 1.24) n 12

Since it contains zero we cannot claim that the difference is significant.

Reported Height 68 71 63 70 71 60 65 64 54 63 66 72 Measured Height 67.9 69.9 64.9 68.3 70.3 60.6 64.5 67 55.6 74.2 65 70.8 Difference D 0.1 1.1 -1.9 1.7 0.7 -0.6 0.5 -3 -1.6 -11.2 1 1.2 4. Example 4, page 559 Hypothesis Test for Effect of Marijuana Use on College Students In a study of the effect of marijuana use, light and heavy users of marijuana in college were tested for memory recall, with the results given below (based on data from “The Residual Cognitive Effects of Heavy Marijuana Use in College Students” by Pope and Yurgelun-Todd, Journal of the American Medical Association, Vol. 275, No. 7). Use a 0.05 significance level to test the claim that the population of heavy marijuana users has a standard deviation different from that of light users.

Items sorted correctly by light marijuana users: n = 64, x = 53.3, s = 3.6 Items sorted correctly by heavy marijuana users: n = 65, x = 51.3, s = 4.5

2 2 H0:s 1= s 2 2 2 H0:s 1 s 2 a = 0.05

Critical value: F < F(0.025, 63, 64) = 0.61 or F > F(0.975, 63, 64) = 1.64

2 2 s1 3.6 Test statistic F =2 = 2 = 0.64 s2 4.5

Conclusion: Since 0.61 < 0.64 < 1.64 we fail to reject H0 and conclude that the observed difference in standard deviations is not significant.

BONUS: (Maximum of 5 points)

Problem 9, page 559