Question

Classic Golf Inc. manages five courses in the Jacksonville, Florida, area. The director of golf 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		130
Tuesday		120
Wednesday		110
Thursday		140
Friday		125

At the 0.05 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.

State the decision rule, using the 0.05 significance level.

Compute the value of chi-square.

What is your decision regarding H₀?

Answer 1

Answer:

The given data is,

Day	Rounds (fo)
Monday	130
Tuesday	120
Wednesday	110
Thursday	140
Friday	125

Step 1: Set the null and alternate hypotheses

The null and alternate hypotheses can be stated as:

H₀: Rounds played is the same for each day.

H₁: Rounds played is not the same.

Step 2: Determine the appropriate statistical test

The appropriate test statistic is

where, f_o = observed frequencies and f_e = expected frequencies.

with df = k - 1 - c

Step 3: Set the level of significance

Alpha has been specified as 0.05.

Step 4: Set the decision rule

For a given level of significance 0.05, rules for acceptance or rejection of null hypothesis are as below:

If , reject the null hypothesis, otherwise, do not reject the null hypothesis.

The critical value is where degrees of freedom = n - 1 = 5 - 1 = 4.

Step 5: Analyse the data

Expected frequencies can be computed by dividing total observed frequencies by number of days. In this case, expected frequency =

Day	fo	fe
Monday	130	125	0.2
Tuesday	120	125	0.2
Wednesday	110	125	1.8
Thursday	140	125	1.8
Friday	125	125	0
Total			4

So,

Step 6: Arrive at a statistical conclusion:

At 95% confidence level, the critical value obtained from the table is . Calculated value 4, which is less than the tabular value and falls in the acceptance region. Hence, the null hypothesis is accepted and the alternative hypothesis is rejected. Therefore, we conclude that rounds played is the same for each day.