# Single Sample and Dependent Samples Statistics Questions

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Explanation & Answer length: 10 questions.

Single Sample and Dependent Samples t HOMEWORK Statistics for the Behavioral Sciences On a separate piece of paper, show all of your work and be neat. 1. What determines whether a t test or a Z test should be used? 2. How does the formula for the t test differ from the formula for the Z test? 3. How do critical values of t compare with critical values of Z? If you mistakenly used a Z test rather than a t test, would you be more or less likely to make a Type I error? Why? 4. A researcher hypothesizes that people who listen to music via headphones have greater hearing loss than those in the general population. On a standard hearing test, the mean is 22.5 (higher scores indicate better hearing). The researcher gave this same test to a random sample of 12 individuals who regularly use headphones. Their scores on the test appear below. Test the null hypothesis at the .05 level of significance. If appropriate (because the null hypothesis is rejected), construct a 95 percent confidence interval for the population mean, based on the sample mean. 16, 14, 20, 12, 25, 22, 23, 19, 17, 17, 21, 20 5. Researchers are interested in whether the pulse of long-distance runners differs from that of other athletes.

They obtain a random sample of 8 longdistance runners, measure their resting pulse, and obtain the following data: 45, 42, 64, 54, 58, 49, 47, 55. The average resting pulse of athletes in the general population is 60 beats per minute. Test the null hypothesis at the .01 level of significance. If appropriate (because the null hypothesis is rejected), construct a 99 percent confidence interval for the population mean, based on the sample mean. 6. How does increasing sample size affect a t test? Why does it affect it in this manner? 7. A researcher is interested in whether participating in sports influences selfesteem in young girls. She identifies a group of girls who have not played sports before, but are planning to begin participating in organized sports. She gives them a 50-item self-esteem inventory before they begin playing sports and administers it again after six months of playing sports. The self-esteem inventory is measured on an interval scale, with higher numbers indicating higher selfesteem. In addition, scores on the inventory are normally distributed.

The scores appear below. Test the null hypothesis using the .01 level of significance. If appropriate (because the null hypothesis is rejected), construct a 99 percent confidence interval for the population mean, based on the sample mean. Before After 44 46 40 41 39 41 42 43 43 45 46 47 8. Four individuals with high levels of cholesterol went on a special diet, avoiding high cholesterol foods and taking special supplements. Using the .01 level of significance, was there a significant decrease in cholesterol level? If appropriate, construct a 99 percent confidence interval for the population mean, based on the sample mean. Their total cholesterol levels before and after the diet were as follows: Before After 287 255 305 269 243 245 309 247 9. Give an example of a repeated measures study. Give an example of a related measures study. 10. Five people who were convicted of speeding were ordered by the court to attend a workshop. A special device put into their cars kept records of their speeds for 2 weeks before and after the workshop. Using the .05 level of significance, should you conclude that people are likely to drive more slowly after such a workshop? If appropriate, construct a 95 percent confidence interval for the population mean, based on the sample mean. Before After 65 58 62 65 60 56 70 66 68 60

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