Consider determining whether the population from which n = 50 data points are ga

Question

Consider determining whether the population from which n = 50 data points are gathered follows a uniform distribution (0, 50). You have plotted the data in a frequency histogram with 5 cells of equal width. The histogram of your gathered data is shown below. Perform a Goodness-of-Fit Test with alpha = 0.10 to determine whether the data do not follow a uniform distribution (0, 50). Show the null hypothesis, the alternative hypothesis, the test statistic, the rejection region, the p-value, and give an appropriate conclusion.

Explanation / Answer

null hypothesis: data is uniformly distributed

alternate: data is not unifomly distributed

here test stat chi square =7.60

rejection region at alpha =0.1 is chi critical =7.78

p value for above chi square =0.1073

as chi critical is greater then chi square test stat, we can not reject null hypothesis

observed Expected Chi square AR P O E=total*p =(O-E)^2/E 0-10 0.2 7 10 0.90 10-20 0.2 9 10 0.10 20-30 0.2 15 10 2.50 30-40 0.2 14 10 1.60 40-50 0.2 5 10 2.50 50 50 7.60

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