A normal distribution is a common assumption underlying many statistical tests.

Question

A normal distribution is a common assumption underlying many statistical tests. Although the assumption is usually not important, it is possible to test whether it is plausible. Specifically, the unit normal table lists proportions for individual sections of a normal distribution, and a chi-square test for goodness of fit can be used to evaluate whether a specific distribution fits the proportions. For example, if a normal distribution is divided into sections using z-score values, then proportions in each section should be as follows: -1.5

Explanation / Answer

applying chi square goodness of fit:

at 0.05 level and 4 degree of freedom ' critical value =9.4877

as chi stat 2.9116 is lower then critical value we can not conclude that above sample is significantly different from normal distribution

observed Expected Chi square X Probability O E=total*p =(O-E)^2/E 0 0.0668 8.000 6.01 0.66 1 0.2417 19.000 21.75 0.35 1 0.3830 31.000 34.47 0.35 2 0.2417 23.000 21.75 0.07 3 0.0668 9.000 6.01 1.49 1 90 90 2.9116

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