Question

A die was rolled 600 times with the following results. Use the Chi-square Goodness of Fit Test to test whether the die is balanced. Use a significance level of 0.05. Give the null and alternative hypotheses, test statistic value, decision rule, and p-value.

value

1 2 3 4 5 6

Frequency

87 96 108 89 122 98

Answer 1

Solution:

Given: A die was rolled 600 times with the following results.

We have to use the Chi-square Goodness of Fit Test to test whether the die is balanced.

Level of significance = 0.05

Step 1) State the null and alternative hypotheses.

H0: the die is balanced

Vs

H1: the die is not balanced

Step 2) test statistic value:

Chi square test statistic for goodness of fit

Where

O_i = Observed Counts

E_i =Expected Counts = N / k = 600 / 6 = 100

Outcomes	Oi: Observed frequency	Ei: Expected Frequency	Oi2/Ei
1	87	100	75.69
2	96	100	92.16
3	108	100	116.64
4	89	100	79.21
5	122	100	148.84
6	98	100	96.04
	N = 600

Thus

Step 3) Decision rule

Reject null hypothesis H0, if P-value < 0.05 Level of significance , otherwise we fail to reject H0.

Step 4) P-value:

df = k - 1 = 6 -1 = 5

Look in Chi-square table for df = 5 row and find an interval in which fall, then corresponding right tail area is P-value.

fall between 1.610 and 9.236

corresponding right tail area is between 0.100 and 0.900

thus 0.100 < P-value < 0.900

or P-value > 0.100

Since P-value > 0.100 > 0.05 level of significance, we reject H0.

Thus there is not sufficient evidence to conclude that: the die is balanced.