Question

Workers and​ senior-level bosses were asked if it was seriously unethical to monitor employee​ e-mail. The results are summarized in the table to the right. Use a 0.05 significance level to test the claim that the response is independent of whether the subject is a worker or a boss. Yes No Workers 193 193 241 241 Bosses 36 36 86 86 a. State the null and the alternative hypotheses. Choose the correct answer below. A. The null​ hypothesis: Response is independent of whether the subject is a worker or a​ senior-level boss. The alternative​ hypothesis: There is some relationship between response and whether the subject is a worker or a​ senior-level boss.

Your answer is correct. B. The null​ hypothesis: There is some relationship between response and whether the subject is a worker or a​ senior-level boss. The alternative​ hypothesis: Response is independent of whether the subject is a worker or a​ senior-level boss. b. Assuming independence between the two​ variables, find the expected frequency for each cell of the table.

Table of expected frequencies Yes No Workers nothing nothing Bosses nothing nothing ​(Round to the nearest tenth as​ needed.)

Answer 1

Solution:

Here, we have to use chi square test for independence of two categorical variables.

Null hypothesis: H₀: Response is independent of whether the subject is a worker or a​ senior-level boss.

Alternative hypothesis: H_a: There is some relationship between response and whether the subject is a worker or a​ senior-level boss.

We are given level of significance = α = 0.05

Test statistic formula is given as below:

Chi square = ∑[(O – E)^2/E]

Where, O is observed frequencies and E is expected frequencies.

E = row total * column total / Grand total

We are given

Number of rows = r = 2

Number of columns = c = 2

Degrees of freedom = df = (r – 1)*(c – 1) = 1*1 = 1

α = 0.05

Critical value = 3.841459

(by using Chi square table or excel)

Calculation tables for test statistic are given as below:

Observed Frequencies
	Response
Subject	Yes	No	Total
Workers	193	241	434
Bosses	36	86	122
Total	229	327	556

Expected Frequencies
	Response
Subject	Yes	No	Total
Workers	178.7518	255.2482	434
Bosses	50.2482	71.7518	122
Total	229	327	556

Calculations
(O - E)
14.2482	-14.2482
-14.2482	14.2482

(O - E)^2/E
1.135716	0.795348
4.040169	2.829354

Chi square = ∑[(O – E)^2/E] = 8.800588

Chi square test statistic = 8.8

P-value = 0.003011

(By using Chi square table or excel)

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that there is some relationship between response and whether the subject is a worker or senior-level boss.