1 Comparing The T And The Z Statistics You Can Use Both The T Statistic And The Z Statistic To Test Hypotheses About Th 1 (25.01 KiB) Viewed 40 times
1 Comparing The T And The Z Statistics You Can Use Both The T Statistic And The Z Statistic To Test Hypotheses About Th 2 (25.01 KiB) Viewed 40 times
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1 Comparing The T And The Z Statistics You Can Use Both The T Statistic And The Z Statistic To Test Hypotheses About Th 3 (26.73 KiB) Viewed 40 times
1. Comparing the t and the z statistics You can use both the t statistic and the z statistic to test hypotheses about the mean of population. The test that uses the t statistic is typically referred to as a t test, while the test that uses z statistic is commonly called a z test. Which of the following statements are true of the t statistic? Check all that apply. The t statistic uses the same formula as the z statistic except that the t statistic uses the estimated standard error in the denominator. The t statistic does not require any knowledge of the population standard deviation. The formula for the t statistic is t= (M-u) / OM. The t statistic provides an excellent estimate of z, particularly with small sample sizes. With the exception of whether the population standard deviation is known, the necessary assumptions for hypothesis tests with the t statistic and with the z statistic are
5. Factors that influence a hypothesis test with the t statistic Suppose you conduct a hypothesis test about a population mean when the standard deviation is unknown by calculating a t statistic and determining whether to reject the null hypothesis. Assume that your t statistic is a positive value and that you will reject the null hypothesis when it is very large. For each of the potential changes to the components of your study design or the results listed below, determine the change to the t statistic, and then select "Increases," "Decreases," or "Stays the same from the dropdown menu in the right-hand column. Change in Study Design or Results A switch from using a two-tailed test to a one-tailed test A decrease in the sample standard deviation (s) An increase in the significance level (such as using a = .05 instead of a = .01) A decrease in the sample size (n) The t statistic Stays the same Decreases
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