A variable contains five categories.It is expected that data are uniformly distributed across these five categories.To test this, a sample of observed data is gathered on this variable resulting in frequencies of 26, 10, 17, 21, and 26.Using $\alpha$ = .10, the appropriate decision is ___.
A)do not reject the null hypothesis that the observed distribution is uniform
B)do not reject the null hypothesis that the observed distribution is not uniform
C)reject the null hypothesis that the observed distribution is uniform
D)reject the null hypothesis that the observed distribution is not uniform
E)do nothing

Question

Quizplus · Accepted Answer

We can use the chi-square goodness of fit test to test for uniform distribution. The null hypothesis is that the observed distribution is uniform. We calculate the expected frequencies in each category by dividing the total sample size (100) by the number of categories (5) to get 20. We then calculate the chi-square statistic by summing [(observed frequency - expected frequency)^2 / expected frequency] for each category. This gives us a chi-square statistic of 15.8. The degrees of freedom is (number of categories - 1), which is 4. Using a significance level of .10 and looking at a chi-square table with 4 degrees of freedom, the critical value is 9.488. Since our calculated chi-square value (15.8) is greater than the critical value (9.488), we reject the null hypothesis that the observed distribution is uniform. Therefore, the appropriate decision is to reject the null hypothesis that the observed distribution is uniform (choice C).

A Variable Contains Five Categories α\alphaα = 10, the Appropriate Decision Is ___

A Variable Contains Five Categories $\alpha$ = 10, the Appropriate Decision Is ___