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The testing of hypothesis allows for the use of assumptions about the variables that are being used when it comes to its distribution. The assumptions are considered when the test is chosen and in the interpretation of data. The z test assumes that the distribution of data is normal and that the sampling of data is independent. The z test strength is quite high especially where the size of the sample is big. The test is used in the determination of whether the mean of two populations is different where the sample used in big and the variance is identified (Sherri, 2015). For accuracy in the calculation of the test, the standard deviation of the group should be known.
In testing of the hypothesis of the two populations both the alternative and the null should be indicated that helps in making conclusive results. Where the standard deviation of the sample is identified, then assumption that the variance of the population and the variance of the sample are equal is concluded. The importance of the z test is placed in the ability to determine the variables used in predicting the outcome of a regression analysis and analysis in profit that helps in effecting the responses that one expects. When the null hypothesis is used, it is concluded that there is significance of the predictor variable. Another importance is placed on the testing of Poisson rates and proportion tests where the z-test is used in approximation of the variables. The validity of the approximations is when the size of the sample is large and numerous events are expected. The standard deviations s1 and s2 is used where σ1 and σ2 are not known and when one assumes that the normal distribution is present (Parkinson, 2013).
Sherri L., J. (2015). Research Methods and Statistics: A Critical Thinking Approach. Cengage Learning
Parkinson, M. (2013). z Test for the significance of the mean of a stable probability distribution with 1<α≤2. Journal Of Applied Statistics, 40(3), 465-482.