2. What are the primary advantages of a repeated-measures design over an independent-measures design?

6. The results of two repeated-measures studies are summarized as follows: The first study produces a sample with MD = 4 and s= 9, and the second study produces MD = 12 and s = 9. Assume n = 10 for both samples. In each case, the sample mean and sample
standard deviation should provide enough information for you to visualize (or sketch) the sample distribution.

a. For each sample, identify where a value of zero is located. (Is zero in the middle of the sample or is it an extreme, unrepresentative value for the sample?)

b. Assuming that the samples are representative of their populations, which of the two samples is more likely to have come from a population with a mean difference of \({{\mu }_{D}}\) = 0? (Which sample is more likely to accept a null hypothesis that \({{\mu }_{D}}\) = 0?)

10. Research has shown that losing even one night’s sleep can have a significant effect on performance of complex tasks such as problem solving (Linde & Bergstroem, 1992). To demonstrate this phenomenon, a sample of n = 20 college students was given a
problem-solving task at noon on one day and again at noon on the following day. The students were not permitted any sleep between the two tests. For each student, the difference between the first and second score was recorded. For this sample, the students
averaged MD = 6.3 points better on the first test, with SS for the difference scores equal to 2375.

a. Do the data demonstrate a significant change in problem-solving ability? Use a two-tailed test with \(\alpha =0.05\)

b. Compute an estimate d to measure the size of the effect.

2. Explain why it would not be reasonable to use estimation after a hypothesis test for which the decision was fail to reject Ho.

6. A sample of n = 9 scores is obtained from an unknown population. The sample mean is M = 46 with a standard deviation of s = 6.

a. Use the sample data to make an 80 % confidence interval estimate of the unknown population mean.

b. Make a 90% confidence interval estimate of \(\mu \)

c. Make a 95 % confidence interval estimate of \(\mu \).

d. In general, how is the width of a confidence interval related to the percentage of confidence?

10. Standardized measures seem to indicate that the average level of anxiety has increased gradually over the past 50 years (Twenge, 2000). In the 1950s, the average score on the Child Manifest Anxiety Scale was \(\mu \) = 15.1. A sample of n = 16 of today’s children produces a mean score of M = 23.3 with SS = 240.

a. Based on the sample, make a point estimate of the population mean anxiety score for today’s children.

b. Make a 90% confidence interval estimate of today’s population mean. In what circumstances is the t statistic used instead of a z-score for a hypothesis test?

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