Population Standard Deviation Essay

1. Z- test is used when the sample size is large enough n>30, the population standard deviation is known, and population is normally distributed.
Example: Is the mean of systolic blood pressure level for women use of oral contraceptives is identical with women does not use of oral contraceptives, the sample mean > 30, we known the population standard deviation and it is normally distributed.
H0: µ1=µ2
H1: µ1≠µ2 2. t- test is used when the population standard deviation is not known, the sample size is less than 30, and the underlying population is normally distributed.
Example: Is the mean of systolic blood pressure level for women use of oral contraceptives is identical with women does not use of oral contraceptives, the sample mean < 30, …show more content…
ANOVA test is used when we compare between more than two independent populations.
Example: Is the mean of systolic blood pressure level for more than two groups are same: such as women use of oral contraceptives for 6month, women use of oral contraceptives for 12 months, women use of oral contraceptives for 18 months. These samples are independent.
H0: μ 1= μ 2= …= μ k
H1: At least one mean different

4. Wilcoxon Signed-Rank Test is used to compare two samples from populations that are not independent, and to evaluate the null hypothesis that in the underlying population of differences among pairs, the median difference is equal to 0. It does not require that the population of differences be normally distributed.
Example: Is the mean of systolic blood pressure level for women before use of oral contraceptives are identical with systolic blood pressure level after using oral contraceptives for 18 months. The samples are dependent.
H0: µ1=µ2
H1: µ1≠µ2

5. Wilcoxon Rank Sum Test is used to compare two samples that have been drawn from independent populations and to evaluate the null hypothesis that the medians of the two populations are identical. It does not require that the population be normally