Hypothesis Testing of Single Mean and Single Proportion: Decision and Conclusion 1.4 2008/06/06 17:36:01 GMT-5 2008/07/18 13:54:50.171 GMT-5 Barbara Illowsky illowskybarbara@deanza.edu Susan Dean deansusan@deanza.edu Connexions cnx@cnx.org elementary statistics A systematic way to make a decision of whether to reject or not reject the null hypothesis is to compare the p-value and a preconceived α (also called a "significance level"). A preconceived α is the probability of a Type I error (rejecting the null hypothesis when the null hypothesis is true). It may or may not be given to you at the beginning of the problem.When you make a decision to reject or not reject Ho, do as follows: If α>p-value, reject Ho. The results of the sample data are significant. There is sufficient evidence to conclude that Ho is an incorrect belief and that the alternative hypothesis, Ha, may be correct. If α≤p-value, do not reject Ho. The results of the sample data are not significant. There is not sufficient evidence to conclude that the alternative hypothesis, Ha, may be correct. When you "do not reject Ho", it does not mean that you should believe that Ho is true. It simply means that the sample data has failed to provide sufficient evidence to cast serious doubt about the truthfulness of Ho. Conclusion: After you make your decision, write a thoughtful conclusion about the hypotheses in terms of the given problem. Hypothesis A statement about the value of a population parameter. In case of two hypotheses, the statement assumed to be true is called null hypothesis (notation H0 size 12{H rSub { size 8{0} } } {}) and contradictory statement is called alternate hypothesis (notation Ha size 12{H rSub { size 8{a} } } {}). 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. Type 1 Error The decision is to reject Null hypothesis, when, in fact, Null hypothesis is true.