# Question: How important is the assumption the sampled population is normally

How important is the assumption "the sampled population is normally distributed" for the use of the chi-square distributions? Use a computer and the two sets of MINITAB commands that can be found in the Student Solutions Manual to simulate drawing 200 samples of size 10 from each of two different types of population distributions. The first commands will generate 2000 data values and construct a histogram so that you can see what the population looks like. The next commands will generate 200 samples of size 10 from the same population; each row represents a sample. The following commands will calculate the standard deviation and _2_for each of the 200 samples. The last commands will construct histograms of the 200 sample standard deviations and the 200 _2_-values. (Additional details can be found in the Student Solutions Manual.) For the samples from the normal population:
a. Does the sampling distribution of sample standard deviations appear to be normal? Describe the distribution.
b. Does the _2-distribution appear to have a chi-square distribution with df = 9 ? Find percentages for intervals (less than 2, less than 4, . . ., more than 15, more than 20, etc.), and compare them with the percentages expected as estimated using Table 8 in Appendix
B. For the samples from the skewed population:
c. Does the sampling distribution of sample standard deviations appear to be normal? Describe the distribution.
d. Does the _2-distribution appear to have a chi-square distribution with ? Find percentages for intervals (less than 2, less than 4, . . . , more than 15, more than 20, etc.), and compare them with the percentages expected as estimated using Table 8. In summary:
e. Does the normality condition appear to be necessary in order for the calculated test statistic _2_ to have a _2-distribution? Explain.

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