10th Edition

ISBN: 9780321989178

Author: Neil A. Weiss

Publisher: PEARSON

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In a 2-proportion test, two separate proportions are measured at the same time, and their similarity is evaluated. It is also known as a 2-proportion z-test, and a comparison of two different proportions is done in this method.

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Chapter B.1, Problem 25E

Hip Fracture Rates. In the paper “Very Low Rates of Hip Fracture in Beijing, People’s Republic of China,” L. Xu, A. Lu, X. Zhao, X. Chen, and S. Cummings present the results of a study on the rates of hip fracture for women and men in Beijing for the years 1990–1992 (American Journal of Epidemiology, 144, pp. 901–907). For this analysis, we consider only the hip fracture rates for women.

The following table gives the annual rate of hip fractures (per 100,000 population) for women in 14 age groups.

Chapter B.1, Problem 25E, Hip Fracture Rates. In the paper Very Low Rates of Hip Fracture in Beijing, Peoples Republic of , example 1

To relate hip fracture rate to age, we use the midpoint age for each age group, as depicted in the table. The scatterplot of frac (hip fracture rate) versus age is provided in Output B.20 on page B-29. This scatterplot shows curvature, and we will apply the method of transformations to straighten the scatterplot.

a. In view of Output B.20, which transformations should be attempted on frac? on age?
b. A draftsman plot of powers of frac versus powers of age is shown in Output B.21 on page B-29. Based on these plots, which pairs of transformed variables would you consider for further analysis? Explain your reasoning.
c. The scatterplot of ln (frac) versus age appears to be fairly straight. We performed a regression of ln(frac) on age as shown in Output B.22 on page B-30. Outputs B.23(a) and (b) on page B-31 provide, respectively, a plot of residuals versus lilted values and a normal probability plot of the residuals. Perform a residual analysis to assess the assumptions of linearity of the regression constancy of the equation, conditional standard deviation, and normality of the conditional distributions. Check for outliers and influential observations.
d. Does your analysis in part (c) reveal any violations of the assumptions for regression inferences? Explain y our answer.
e. Refer to the plot of the regression equation of ln(frac) on age displayed on the scatterplot in Output B.24 on page B-31. Based on this plot and the results of the residual analysis in parts (c) and (d), is the transformation in part (c) effective at straightening the scatterplot? Explain y our answer.

OUTPUT B.20

Scatterplot of frac versus age for Exercise B.25

Chapter B.1, Problem 25E, Hip Fracture Rates. In the paper Very Low Rates of Hip Fracture in Beijing, Peoples Republic of , example 2

Chapter B.1, Problem 25E, Hip Fracture Rates. In the paper Very Low Rates of Hip Fracture in Beijing, Peoples Republic of , example 3

OUTPUT B.21

Draft plot for Exercise B.25

Chapter B.1, Problem 25E, Hip Fracture Rates. In the paper Very Low Rates of Hip Fracture in Beijing, Peoples Republic of , example 4

OUTPUT B.22

Output off regression of ln(frac) on age for Exercise B.25

OUTPUT B.23

Residual plots for Exercise B.25

Chapter B.1, Problem 25E, Hip Fracture Rates. In the paper Very Low Rates of Hip Fracture in Beijing, Peoples Republic of , example 5

OUTPUT B.24

Scatterplot and plot of regression equation for Exercise B.25

Chapter B.1, Problem 25E, Hip Fracture Rates. In the paper Very Low Rates of Hip Fracture in Beijing, Peoples Republic of , example 6

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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Chapter B.1, Problem 24E

Chapter B.1, Problem 26E

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Chapter B Solutions

Introductory Statistics (10th Edition)

Ch. B.1 - Regarding the regression of a response variable,...Ch. B.1 - Fill in the blanks. a. The assumption that all...Ch. B.1 - Answer true or false to each of the following...Ch. B.1 - Prob. 4E Ch. B.1 - In each of Exercises B.5B.14, a. decide whether...Ch. B.1 - Prob. 6E Ch. B.1 - Prob. 7E Ch. B.1 - In each of Exercises B.5B.14, a. decide whether...Ch. B.1 - In each of Exercises B.5B.14, a. decide whether...Ch. B.1 - In each of Exercises B.5B.14, a. decide whether...

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Solution Summary: The author identifies the transformations that should be attempted on in view of Output B.20.

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