The t Statistic•allows researchers to use sample datato test hypotheses about an unknown population mean. •does not require any knowledge of the population standard deviation (needed when using z-score)•can be used to test hypotheses about a completely unknownpopulation; that is, both μand σare unknown, and the only available information about the population comes from the sample.
The t Statistic•required for a hypothesis test using t-stat–a sample –a reasonable hypothesis about the population mean.
The t StatisticTwo general situations where the t-statistic is used in hypothesis testing:1. to determine whether or not a treatment causes a change in a population mean. –must know the value of μfor the original, untreated population–Obtain a sample from the population –the treatment is administered to the sample–If the resulting sample mean is significantly different from the original population mean, can conclude that the treatment has a significant effect
The t Statistic2.a hypothesized valuefor an unknown population mean is derived from a theory or other prediction–Obtain a sample from the population–the t statistic is used to compare the actual sample mean with the hypothesized population mean–significant difference indicates that the hypothesized value for μshould be rejected
The Estimated Standard Error and the t Statistic •sampling error (discrepancy or "error" between the sample mean and the population mean) is expected•Is the discrepancy observed between sample mean and population mean significant? –Find out through hypothesis testings
The Estimated Standard Error and the t StatisticTwo alternatives to consider in hypothesis testing:1.Discrepancybetween M and μis simply due to sampling errorand not resulting from treatment effect OR 2.Discrepancy between M and μmore than what is expected bysampling error alone, therefore the sample mean significantly different from the population mean
The Estimated Standard Error and the t Statistic•The critical first step for the t statistic