Question

1. Perform the indicated goodness-of-fit test.

A company manager wishes to test a union leader's claim that absences occur on the different week days with the same frequencies. Test this claim at the 0.05 level of significance if the following sample data have been compiled.

a. test statistic

b. critical value

2.Perform the indicated goodness-of-fit test.

In studying the responses to a multiple-choice test question, the following sample data were obtained. At the 0.05 significance level, test the claim that the responses occur with the same frequency.

a. test statistic

b. critical value

3. Perform the indicated goodness-of-fit test.

Using the data below and a 0.05 significance level, test the claim that the responses occur with percentages of 15%, 20%, 25%, 25%, and 15% respectively.

a. test statistic

b. critical value

Answer 1

Observed (Oi )	Expected ( Ei)	Oi-Ei	(Oi-Ei)^2	(Oi-Ei)^2/Ei
37	26	11	121	4.6538
15	26	-11	121	4.6538
12	26	-14	196	7.5385
23	26	-3	9	0.3462
43	26	17	289	11.1154

Q1. observed frequncies are Oi 37 15 12 23 43 expected frequencies are Ei 130/5 26 and claiming hypothesis is null, Ho: no association exists b/w them alternative, H1: exists association b/w them level of significance, alpha 0.05 from standard normal table, chi square value at right tailed, ^2 alpha/2 9.4877 since our test is right tailed,reject Ho when ^2 o >9.4877 we use test statistic w^2 o (Oi-Ei)^2/Ei from the table take sum of (Oi-Ei)^2/Ei, we get 4^2o = 28.3077 critical value = the value of |y^2 alphal at los 0.05 with d.f, n - 1 = 5 - 1 = 4 is 9.4877 we got | 2=28.3077 & | ^2 alpha | =9.4877 make decision hence value of | ^2 o | 2 p_value =0 ^2 alphal and here we reject Ho test statistic: 28.3077 critical value: 9.4877