Question

Determine​ (a) the χ2 test​ statistic, (b) the degrees of​freedom, (c) the critical value using alpha equals α=0.05​, and​(d) test the hypothesis at the alpha equals α=0.05 level of significance.

Outcome	A	B	C	D
Observed	48	52	51	49
Expected	50	50	50	50

Ho : Pa = Pb = Pc = Pd = 1/4

H1 : At least one proportions is different from the others.

a) The test statistic is

b) The degrees of freedom are one less than the number of possible outcomes. There are 4 possible outcomes. Therefore, there are 3 degrees of freedom

c) Use a table or technology to find the critical value  , rounding to three decimal places. Remember, there are 3 degrees of freedom and the significance level is a = .05.

d) To decide if the null hypothesis should be rejected, compare the test statistic to the critical value.

Answer 1

a) The chi square test statistic here is computed as:

Therefore 0.2 is the required chi square test statistic value here.

b) The degrees of freedom is already given here as n - 1 = 3

c) For 0.05 level of significance, we have from the chi square distribution tables here:

Therefore 7.82 is the required chi square critical value here.

d) As the test statistic value here is 0.2 < 7.82, therefore it lies in the non rejection region and therefore we cannot reject the null hypothesis here. Therefore we cannot reject the null hypothesis here.