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 $\alpha$ = .01, 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 20 (100/5). The chi-square statistic is calculated as:$\chi^2 = \sum (O_i - E_i)^2 / E_i$where O_i is the observed frequency and E_i is the expected frequency.Plugging in the values, we get:$\chi^2 = (26-20)^2/20 + (10-20)^2/20 + (17-20)^2/20 + (21-20)^2/20 + (26-20)^2/20 = 10$The critical value of chi-square with 4 degrees of freedom and $\alpha$ = .01 is 13.28. Since our calculated chi-square value (10) is less than the critical value, we fail to reject the null hypothesis that the observed distribution is uniform.

A Variable Contains Five Categories α\alphaα = 01, the Appropriate Decision Is ___

A Variable Contains Five Categories $\alpha$ = 01, the Appropriate Decision Is ___