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