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Chapter 15: Problem 11

A researcher randomly assigns college freshmen to either of two experimental conditions. Because both groups consist of college freshmen, someone claims that it is appropriate to use a \(t\) test for the two related samples. Comments?

Short Answer

Expert verified
No, it wouldn't be appropriate to use a \(t\) test for the two related samples, as the two groups of college freshmen are not paired observations. Instead, a \(t\) test for two independent samples should be performed.

Step by step solution

01

Understand the Situation

In this exercise, college freshmen are randomly assigned to two different experimental conditions. We need to identify whether these two groups are related or independent.
02

Analyze the Type of Data

Following up from step 1, we need to take into account if the data obtained from the two groups are obtained from the same sample (i.e., paired observations) or from independent samples. A \(t\) test for related samples demands that data are paired and basically come from the same participants, such as 鈥榖efore鈥� and 鈥榓fter鈥� measurements in a study.
03

Concluding if the t-Test is Applicable

Given the information provided, the college freshmen were randomly assigned into the two groups as independent samples. This infers that the two groups are not paired, and hence a \(t\) test for two related samples would not be appropriate in this case. The correct test should be a \(t\) test for two independent samples.

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Most popular questions from this chapter

Each of the following studies requires a \(t\) test for one or more population means. Specify whether the appropriate \(t\) test is for one sample, two independent samples, or two related samples, and in the last case, whether it involves repeated measures or matched pairs of different subjects. (a) College students are randomly assigned to receive either behavioral or cognitive therapy. After twenty therapeutic sessions, each student earns a score on a mental health questionnaire. (b) A researcher wishes to determine whether attendance at a day-care center increases the scores of three-year-old children on a motor skill test. Random assignment dictates which twin from each pair of twenty twins attends the day- care center and which twin stays at home. (Such a draconian experiment doubtless would incur great resistance from the parents, not to mention the twins!) (c) One hundred college freshmen are randomly assigned to sophomore roommates who have either similar or dissimilar vocational goals. At the end of their first year, the mean GPAs of these two groups are to be analyzed. (d) According to the U.S. Department of Health, the average 16-year-old male can do 23 pushups. A physical education instructor finds that in his school district, 30 randomly selected 16-year-old males can do an average of 28 pushups. (e) A child psychologist assigns aggression scores to each of 10 children during two 60 -minute observation periods separated by an intervening exposure to a series of violent TV cartoons.

In a classic study, which predates the existence of the EPO drug, Melvin Williams of Old Dominion University actually injected extra oxygen-bearing red cells into the subjects' bloodstream just prior to a treadmill test. Twelve long-distance runners were tested in 5 -mile runs on treadmills. Essentially, two running times were obtained for each athlete, once in the treatment or blood-doped condition after the injection of two pints of blood and once in the placebo control or non-blood-doped condition after the injection of a comparable amount of a harmless red saline solution. The presentation of the treatment and control conditions was counterbalanced, with half of the subjects unknowingly receiving the treatment first, then the control, and the other half receiving the conditions in reverse order. Since the difference scores, as reported in the New York Times, on May 4,1980 , are calculated by subtracting blood-doped running times from control running times, a positive mean difference signifies that the treatment has a facilitative effect, that is, the athletes' running times are shorter when blood doped. The 12 athletes had a mean difference running time, \(\bar{D}\), of 51.33 seconds with a standard deviation, \(s_{D}\), of 66.33 seconds. (a) Test the null hypothesis at the .05 level of significance. (b) Specify the \(p\) -value for this result. (c) Would you have arrived at the same decision about the null hypothesis if the difference scores had been reversed by subtracting the control times from the blooddoped times? (d) If appropriate, construct and interpret a 95 percent confidence interval for the true effect of blood doping. (e) Calculate and interpret Cohen's \(d\) for these results. (f) How might this result be reported in the literature? (g) Why is it important to counterbalance the presentation of blood-doped and control conditions? (h) Comment on the wisdom of testing each subject twice- once under the blooddoped condition and once under the control condition- during a single 24 -hour period. (Williams actually used much longer intervals in his study.)

A random sample of 38 statistics students from a large statistics class reveals an \(r\) of -.24 between their test scores on a statistics exam and the time they spent taking the exam. Test the null hypothesis with \(t\), using the .01 level of significance.

Indicate whether each of the following studies involves two independent samples or two related samples, and in the latter case, indicate whether the study involves repeated measures for the same subjects or matched pairs of different subjects. (a) Estimates of weekly TV-viewing time of third-grade girls compared with those of thirdgrade boys (b) Number of cigarettes smoked by participants before and after an antismoking workshop (c) Annual incomes of husbands compared with those of their wives (d) Problem-solving skills of recognized scientists compared with those of recognized artists, given that scientists and artists have been matched for \(\mathbb{Q}\)

In Table 7.4 on page 142 , seven of the ten top hitters in the major league baseball in 2014 had lower batting averages in \(2015,\) supporting regression toward the mean. Treating averages as whole numbers (without decimal points) and subtracting their batting averages for 2015 from those for 2014 (so that positive difference scores support regression toward the mean), we have the following ten difference scores: 28,53,17,37,27,27,22,-25,-7,0. (a) Test the null hypothesis (that the hypothetical population mean difference equals zero for all sets of top ten hitters over the years) at the .05 level of significance. (b) Find the \(p\) -value. (c) Construct a 95 percent confidence interval. (d) Calculate Cohen's \(d\). (e) How might these findings be reported?
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