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# Student's t test and Z test

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1. What factor determines whether you should use a z-score or a t statistic for a hypothesis test?

2. Several factors influence the value obtained for a t statistic. Some factors affect the numerator of the t statistic and others influence the size of the estimated standard error in the denominator. For each of the following, indicate whether the factor influences the numerator or denominator of the t statistic and determine whether the effect would be to increase the value of t (farther from zero). In each case, assume that all other factors remain constant.
a. Increase the variability of the scores.
b. Increase the number of scores in the sample.
c. Increase the difference between the sample mean and the population mean.

5. A sample of n=16 scores has a mean of M=45 and SS=960.
a. Calculate the sample standard deviation (s) and the estimated standard error for the sample mean (Sm).
b. Describe what is measured by the standard deviation and what is measured by the estimated standard error.

14. The herbal supplement ginkgo biloba is advertised as producing an increase in physical strength and stamina. To test this claim, a sample of n=36 adults is obtained and each person is instructed to take the regular daily dose of the herb for a period of 30 days. At the end of the 30-day period, each person is tested on a standard treadmill task for which the average, age-adjusted score is ? =15. The individuals in the sample produce a mean score of M=16.9 with ss=1260.
a. Are these data sufficient to conclude that the herb has a statistically significant effect using a two-tailed test with â??=.05? (Assume that the herb is expected to increase scores.)
b. What decision would be made if the researcher used a one-tailed test with â??=.05? (Assume that the herb is expected to increase scores.)