# Applied Statistics Groups Variance Calculation Exercise Homework Help

*label*Mathematics

*timer*Asked: Mar 4th, 2019

*account_balance_wallet*$9.99

### Question Description

1. A study of patients with insulin-dependent diabetes was conducted to investigate the effects of cigarette smoking on renal and retinal complications. Before examining the results of the study, you wish to compare the baseline measures of systolic blood pressure across four different subgroups: nonsmokers, current smokers, ex-smokers, and tobacco chewers. A sample is selected from each subgroup; the relevant data are shown below. Means and standard deviations are expressed in mm Hg. Assume that systolic pressure is normally distributed.

n mean

standard deviation Nonsmokers 269 115 13.4 Current Smokers 53 114 10.1 Ex-smokers 28 118 11.6 Tobacco Chewers 9 126 12.2

(a) Calculate the estimate of the within-groups variance. (b) Calculate the estimate of the between-groups variance. (c) At the 0.05 level significance, test the null hypothesis that the mean systolic blood pressures of the four groups are identical. What do you conclude? (d) If you find that the population means are not equal, one approach to doing multiple comparisons is the Bonferroni procedure. What would the significance level of each individual test be if this method were used?

2. The data set lowbwt contains information for a sample of 100 low birth weight infants born in two teaching hospitals in Boston. Systolic blood pressure measurements are saved under the variable name sbp and gender under the name sex.

(a) Assuming equal variances for males and females, use the two-sample t-test to evaluate the null hypothesis that among low birth weight infants, the mean systolic blood pressure for girls is identical to that for boys. (b) Even though there are only two populations instead of three or more, test the same null hypothesis using the one-way analysis of variance. (c) In the book, the statement has been made that in the case of two independent samples, the F-test used in the one-way analysis of variance reduces to the twosample t-test. Do you believe this to be true? Explain briefly.

## Tutor Answer

Brown University

1271 Tutors

California Institute of Technology

2131 Tutors

Carnegie Mellon University

982 Tutors

Columbia University

1256 Tutors

Dartmouth University

2113 Tutors

Emory University

2279 Tutors

Harvard University

599 Tutors

Massachusetts Institute of Technology

2319 Tutors

New York University

1645 Tutors

Notre Dam University

1911 Tutors

Oklahoma University

2122 Tutors

Pennsylvania State University

932 Tutors

Princeton University

1211 Tutors

Stanford University

983 Tutors

University of California

1282 Tutors

Oxford University

123 Tutors

Yale University

2325 Tutors