All hypothesis tests represent variations on a common theme. If some observed characteristic, such as the mean for a random sample, qualies as a rare outcome under the null hypothesis, the hypothesis will be (8) .Otherwise, the hypothesis will be (9) To determine whether an outcome is rare, the observed characteristic IS converted to a new value, such as t, and compared to critical values from the appropriate sampling distribution. To construct condence intervals for estimating the population mean based on a t distribution, use the formula for condence intervals previously presented and substitute t for z. The symmetrical limits of a condence interval require specications like those of a twotailed hypothesis test. Use of the t test requires some basic assumptions. Use t rather than 2 when the (10) is unknown. Assume that the underlying population is (11) . If the assumption of normality is violated, the accuracy of the test is relatively unaffected as long as (12) is sufficient