A variable contains four categories.It is expected that data are uniformly distributed across these four categories.To test this, a sample of observed data is gathered on this variable resulting in frequencies of 22, 35, 32, and 21.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

The expected frequency for each category is 25 (100/4). The chi-square statistic is calculated as:$\chi^2 = \frac{(22-25)^2}{25} + \frac{(35-25)^2}{25} + \frac{(32-25)^2}{25} + \frac{(21-25)^2}{25} = 6.4$The critical value of chi-square with 3 degrees of freedom and $\alpha$ = .10 is 6.251. Since the calculated chi-square value (6.4) is greater than the critical value (6.251), we reject the null hypothesis that the observed distribution is uniform.

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

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