Question

Emerald Golf Club in Thailand manages five courses in the Phuket area. The main boss of Emerald Golf Club wishes to study the number of rounds of golf played per weekday at the five courses. He gathered the following sample information.

Day	Rounds
Monday		120
Tuesday		105
Wednesday		100
Thursday		150
Friday		150

At the 0.01 significance level, is there a difference in the number of rounds played by day of the week?

H₀: Rounds played is the same for each day.
H₁: Rounds played is not the same.

Answer 1

Solution:

Here, we have to use chi square test for goodness of fit.

Null hypothesis: H0: Rounds played is the same for each day.

Alternative hypothesis: Ha: Rounds played is not the same.

We are given level of significance = α = 0.01

We are given

Number of categories/days = N = 5

Degrees of freedom = df = N - 1 = 4

α = 0.01

Critical value = 13.27670414

(by using Chi square table or excel)

Test statistic formula is given as below:

Chi square = ∑[(O – E)^2/E]

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

Calculation tables for test statistic are given as below:

Day	O	E	(O - E)^2/E
Monday	120	125	0.2
Tuesday	105	125	3.2
Wednesday	100	125	5
Thursday	150	125	5
Friday	150	125	5
Total	625	625	18.4

Test Statistic = Chi square = ∑[(O – E)^2/E] = 18.4

χ2 = 18.4

P-value = 0.001030602

(By using Chi square table or excel)

P-value < α = 0.01

So, we reject the null hypothesis

There is sufficient evidence to conclude that there is a difference in the number of rounds played by day of the week.