![]() ![]() (b) The sample can only have two outcomes. (a) We must know that the sample is representative so that there is no bias in the test. ![]() Like the null hypothesis, the alternate hypothesis is also stated in contextually meaningful words.) 2) After stating the null and alternate hypothesis, some conditions must be analyzed in order to ascertain the validity of the test. This is why the symbols show that the proportion is either not equal to, is less than, or is greater than the proportion stated in the null hypothesis. It must always be in contradiction to the null hypothesis. Additionally, the null hypothesis must be stated in such a way that it can be contradicted.) (The alternate hypothesis is what we hope to say is true about the population. Moreover, it will state in contextually meaningful words what trait the proportion is representing as the truth. The test is accomplished in five steps: 1) (The null hypothesis states that the proportion "p" is equal to a decimal fraction ".x" of the population. ![]() ![]() This justifies rejecting the null hypothesis and accepting the alternative hypothesis. The philosophical concept behind the test can be stated as, “If the sample proportion obtained by random sampling is not very likely if the null hypothesis is true, then the null hypothesis must not be very likely to be true.” In other words, the true proportion probably lies somewhere closer to the sample proportion. Therefore, the null hypothesis is simply set up as the straw man for the purpose of being able to reject it in order that the alternate can be accepted. The other hypothesis is called the “alternative hypothesis.” This is the hypothesis that is hoped to be accepted. It begins with a hypothesis called a “null hypothesis” stating either the conventional wisdom if there is conventional wisdom on the subject, or the boring assumption that the trait in question is not prevalent. The hypothesis test for a single proportion is a test of two contradictory hypotheses about the proportion of the characteristic under question in the population. A hypothesis test for a single proportion measures the proportion of a sample taken from the population for a given trait in order to infer information about the proportion of that trait in the whole population itself. ![]()
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