Question

A beer industry association is interested in determining the preference of workers for light, dark, and regular beers. A survey was conducted in which 300 blue color workers and 300 white color workers, randomly selected from two groups, were given a choice of three different beers. Each worker expressed their favorite. The following results were obtained:

Worker	Light Beer	Dark Beer	Regular Beer
Blue Color	75	50	175
White Color	120	85	95

The value of the chi-square test statistic is:

The critical value of chi-square obtained from the table (or using MS Excel) for a 5% level of significance (alpha) is:

Based on your answers to the previous questions, your decision is to Accept H₀. (True or False):

Answer 1

Solution:

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

Null hypothesis: H0: Two variables are independent.

Alternative hypothesis: Ha: Two variables are dependent.

We assume/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

The critical value of chi-square obtained from the table (or using MS Excel) for a 5% level of significance (alpha) is:

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)

Calculation tables for test statistic are given as below:

Observed Frequencies
	Beer
Color	Light	Dark	Regular	Total
Blue	75	50	175	300
While	120	85	95	300
Total	195	135	270	600

Expected Frequencies
	Beer
Color	Light	Dark	Regular	Total
Blue	97.5	67.5	135	300
While	97.5	67.5	135	300
Total	195	135	270	600

Calculations
(O - E)
-22.5	-17.5	40
22.5	17.5	-40

(O - E)^2/E
5.192308	4.537037	11.85185
5.192308	4.537037	11.85185

The value of the chi-square test statistic is:

Test Statistic = Chi square = ∑[(O – E)^2/E] = 43.16239

χ2 statistic = 43.16239

P-value = 0.0000

(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 two variables are dependent.

Based on your answers to the previous questions, your decision is to Accept H0. (True or False):

Answer: False