Question

Show how to answer this in EXCEL ONLY, NO megastat or minitab, etc.. Please highlight what data tools or formulas were used.

A survey investigated the public’s attitude toward the federal deficit. Each sampled citizen was classified as to whether he or she felt the government should reduce the deficit or increase the deficit, or if the individual had no opinion. The sample results of the study by gender are reported to below.

Gender	Reduce the Deficit	Increase the Deficit	No Opinion
Female	224	194	68
Male	305	114	25

At the .05 significance level, is it reasonable to conclude that gender is independent of a person’s position on the deficit?

Answer 1

Solution:

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

Null hypothesis: H₀: The gender is independent of a person’s position on the deficit.

Alternative hypothesis: H_a: The gender is dependent of a person’s position on the deficit.

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 = 3

Degrees of freedom = df = (r – 1)*(c – 1) = 1*2 = 2

α = 0.05

Critical value = 5.991465

(by using Chi square table or excel)

[Excel command: =CHIINV(0.05, 2)]

Calculation tables for test statistic are given as below:

Observed Frequencies
	Column variable
Gender	Reduce the Deficit	Increase the Deficit	No Opinion	Total
Female	224	194	68	486
Male	305	114	25	444
Total	529	308	93	930

Expected Frequencies
	Column variable
Gender	Reduce the Deficit	Increase the Deficit	No Opinion	Total
Female	276.4452	160.9548	48.6	486
Male	252.5548	147.0452	44.4	444
Total	529	308	93	930

Calculations
(O - E)
-52.4452	33.04516	19.4
52.44516	-33.0452	-19.4

(O - E)^2/E
9.949514	6.784404	7.744033
10.89068	7.426172	8.476577

Chi square = ∑[(O – E)^2/E] = 51.27138

P-value = 0.0000

(By using Chi square table or excel)

[Excel command: =CHIDIST(51.27138, 2)]

P-value < α = 0.05

So, we reject the null hypothesis

There is not sufficient evidence to conclude that the gender is independent of a person’s position on the deficit.