Will the chi-square test ever conclude, at the 5% significance level, that data are not normally distributed when you know that they are?
Check this with simulation.
Specifically, generate n normally distributed numbers with mean 100 and standard deviation 15. You can do this with the formula =NORMINV (RAND(),100,12). Do not freeze them; keep them random. Then run the chi-square normality test on the random numbers. Because the chi-square results are linked to the data, you will get new chisquare results every time you press F9 to recalculate.
a. Using n = 150, do you ever get a p-value less than 0.05? If so, what does such a p-value mean? Would you expect to get a few such p-values? Explain.
b. Repeat part a using n = 1000. Do the results change in any qualitative way?
c. Repeat parts a and b, but use the Lilliefors test instead of the chi-square test. Do you get the same basic results?