Unit 8 Exercises
(Independent Samples and
Their Differences)
(8.1) Study Questions
(A) How do paired and independent samples differ?
(B) Besides independence of groups, what other statistical assumptions are required for
independent t tests?
(C) In plain words, describe the null hypothesis tested by the independent t test.
(D) How might side-by-side boxplot be used to assess whether the equal variance assumption is true?
(E) What is pooled in the pooled estimate of variance.
(F) A 95% confidence interval for an independent mean difference is (-3.3, 1.7). Interpret this
interval.
(G) How can a 95% confidence interval for �1 - �2 be used to test H0: �1 - �2 = 0 at a = .05?
(H) Indicate whether each of the following studies involve independent or paired samples
(Ha) Estimates of weekly TV-viewing of third-grade boys with ADHD compared with those
who do not have ADHD.
(Hb) Cortisol levels of husbands compared with their wives.
(Hc) Scores on psychological stress tests of freshman who plan to major in engineering are
compared with the scores on the stress test of freshman who plan to major in social sciences.
(Hc) Problem-solving skills of scientists are compared with the problem-solving skills of artists
with individuals matched for IQ.
(8.2) PATIENT-SATIS: A study of patient satisfaction in men and women shows no significant difference. You were expecting a mean difference of 0.25. The pooled estimate of standard deviation from this study was 0.67, and the study included 10 men and 10 women. How many men and women should have been studied in order to achieve 80% power? In your opinion, was the power of the initial study (i.e., the study in which n1 = n2 = 10) adequate?
(8.3) TWOGRPS: Symptomatic and asymptomatic HIV-positive men demonstrate the following scores on a psychological profile:
Symptomatic: 86 99 96 95 72 73 95 125 97
95
Asymptomatic: 110 126 89 106 98 105 93 127 130
92
(A) Compare the groups in the form of side-by-side boxplots. In plain language, compare the
locations and spreads of the two distributions.
(B) Calculate the mean and standard deviation of each group.
(C) Perform a test of statistical significance of the difference between the two group means. Let a
= .05. List all hypothesis testing steps and show all calculations. Clearly state the conclusion of
the test.
(8.4) HISTIDINE: The following data represent total histidine excretion levels (milligrams) in 24-hour urine samples from men and women on restricted diets:
Men: 229 236 172 256 204
Women: 197 224 115 174 138 135
(A) Construct side-by-side boxplots of the data. Compare the locations and spreads of the two distributions.
(B) Calculate the mean and standard deviation of each group. Also, report the sample size of each
group. Use statistical notation. Show all work.
(C) Test the data for significance. Show all hypothesis testing steps (H0, H1, etc.) and calculations.
In plain language, using one or two sentences, discuss your results.
(8.5) INDTSIZE: You are planning a study to compare cholesterol levels in vegetarians and non-vegetarians. Previous studies suggest that the standard deviation of cholesterol levels is approximately 40 mg/dl. You want to use an a level of .05 (two-sided), want power to exceed 80%, and have an equal number of subjects in each group. Based on these assumptions, how many subjects should be studied to detect a mean difference of 10 mg/dl?
(8.6) BONE: A study was conducted to determine whether maternal cigarette smoking affects the bone mineral density of newborns. A sample of 77 infants from mothers who smoke had a mean bone mineral content of 0.098 g/cm� (s1 = 0.026 g/cm�). A sample of 161 children whose mothers had not smoked have mean bone mineral content of 0.095 g/cm� (s2 = 0.025 g/cm�). Estimate the mean difference in bone mineral content with 95% confidence (i.e., calculate a 95% confidence interval) and interpret this result.
(8.7) CMV: One theory suggests that cytomegalovirus (CMV) infection contributes to development of restenosis following coronary angioplasty. To test this theory, 75 patients with coronary atherosclerosis undergoing angioplasty were studies following their procedures. Six months after their surgery, the 49 patients who were seropositive for CMV experience an average luminal diameter reduction of 1.24 mm (s1 = 0.83 mm). In contrast, 26 patients who were seronegative for CMV experience an average luminal reduction of 0.68 (s2 = 0.69). Test whether the differences in average luminal reduction was significant. In plain language, summarize your findings.
(8.8) ANXIETY (Rosner, 1990, p. 280; Alarcon, 1982): Severe anxiety occurs often in patients who must undergo chronic hemodialysis. To help counteract this anxiety, a set of progressive relaxation exercises was shown on videotape to a group of 38 experimental subjects. A control group of 23 patients viewed a set of neutral videotapes. Following these interventions, a psychiatric questionnaire (the State-Trait Anxiety Inventory) was administered to both groups. For the experimental group, the mean State-Trait Anxiety Inventory score was 33.42 (standard deviation = 10.18). For the control group, the mean State-Trait Anxiety Inventory was 39.71 (standard deviation = 9.16). Test whether the experimental intervention was effective. Show all hypothesis testing steps, and summarize your results in plain language.
(8.9) ASPIRIN: In a randomized clinical trial of women with pregnancy-induced hypertension, 23 women received aspirin and 24 received a placebo. After several weeks on treatment, the mean arterial blood pressure of the aspirin-treated group was 111 mm Hg (s1 = 8 mm Hg) and the mean blood pressure of the control group was 109 mm Hg (s2 = 8 mm Hg). Perform at test to determine whether aspirin treatment was effective. Include all hypothesis testing steps, and show all work.
(8.10) FEV: Download the data set fev.sav. (The file can be found in the data set directory linked to StatPrimer's home page.) This file contains a variable named FEV, which represents forced expiratory volume. Forced expiratory volume is a measure of respiratory function based on the amount of air a subject can expel through a tube in a given period of time. Use methods learned in this section to compare the forced expiratory volumes in smokers and non-smokers. Include a graphical comparison, summary statistics, and a null hypothesis test in your analysis. Show all work.