Hypothesis Testing of Single Mean and Single Proportion: Summary of the Hypothesis Test 1.2 2008/06/06 17:38:34 GMT-5 2008/07/18 10:28:22.101 GMT-5 Barbara Illowsky illowskybarbara@deanza.edu Susan Dean deansusan@deanza.edu Connexions cnx@cnx.org elementary statistics The hypothesis test itself has an established process. This can be summarized as follows: Determine Ho and Ha. Remember, they are contradictory. Determine the random variable. Determine the distribution for the test. Draw a graph, calculate the test statistic, and use the test statistic to calculate the p-value. (A z-score and a t-score are examples of test statistics.) Compare the preconceived α with the p-value, make a decision (reject or cannot reject Ho), and write a clear conclusion using English sentences. Notice that in performing the hypothesis test, you use α and not β. β is needed to help determine the sample size of the data that is used in calculating the p-value. Remember that the quantity 1-β is called the Power of the Test. A high power is desirable. If the power is too low, statisticians typically increase the sample size while keeping α the same. If the power is low, the null hypothesis might not be rejected when it should be. Hypothesis Testing Based on sample evidence procedure to determine whether the hypothesis stated is a reasonable statement and cannot be rejected, or is unreasonable and should be rejected. p-value The probability that event will happen purely by chance assuming the null hypothesis is true. The smaller p-value, the stronger the evidence is against the null hypothesis.