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Distributions Used for Hypothesis Tests Normal distribution (Z distributions) Hypothesis Testing for a Single Population Mean is known = Z-Test 1. You are given the sample standard deviation 2. You are given the population standard deviation 3. The problem deals with means, not percentages Population standard deviation will always be used to determine the distribution even if the sample standard deviation is given. The homework will ask for the z distribution or the distribution written as : Z ~ N (mean from hypotheses, ππππ’πππ‘πππ π π‘ππππππ πππ£ππ‘πππ βπ πππππ π ππ§π ) OR Hypothesis Testing for a Single Population proportion is known = Prop Z-Test For our class, the only type of hypothesis testing using percentages in the problems will be Prop Z-Test. They use the normal distributions. The homework will ask for the z distribution or the distribution written as : Z ~ Pβ (proportion from hypotheses, standard deviation of the proportion (ππ₯ )) (ππ₯ ) is β πβπ π ο· ο· ο· ο· The p is the proportion used in the hypotheses. So if the percentage is 5.5%, the proportion is 0.055 which means p = 0.055. The q is 1 - p so 1 - 0.055 = 0.945. The n is the sample size which is given in the problem. Let's say it is 100. ο· To solve it β πβπ π =β 0.055β0.945 100 = 0.02279 or 0.023 Studentβs t-distribution Hypothesis Testing for Population Means Ο is unknown = T-Test 1. You are given the sample standard deviation 2. You are NOT given the population standard deviation 3. The problem deals with means, not percentages Since the population standard deviation is not given, you have to use the sample standard deviation. The homework will ask for the t distribution or the distribution written as : π‘ππ where df is degrees of freedom (or sample size -1)