Question

Classic Golf Incorporated 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 145
Tuesday 125
Wednesday 135
Thursday 100
Friday 120
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.

Answer 1

To determine if there is a difference in the number of rounds played by day of the week, a one-way ANOVA (Analysis of Variance) test can be conducted. The null hypothesis (H0) states that the rounds played are the same for each day, while the alternative hypothesis (H1) suggests that there is a difference.

First, calculate the mean number of rounds for each day:

`\[ \bar{X}_M = (145+125+135+100+120)/(5) = 125 \]`

Next, calculate the overall mean
`(\( \bar{X} \))`:

`\[ \bar{X} = (145+125+135+100+120)/(5) = 125 \]`

Now, calculate the between-group sum of squares (SSB) and within-group sum of squares (SSW):

`\[ SSB = \sum_(i=1)^(5) n_i (\bar{X}_i - \bar{X})^2 \]`

`\[ SSW = \sum_(i=1)^(5) \sum_(j=1)^(n_i) (X_(ij) - \bar{X}_i)^2 \]`

Finally, calculate the F-statistic:

`\[ F = (SSB / (k-1))/(SSW / (N-k)) \]`

where k is the number of groups (days) and N is the total number of observations.

Compare the calculated F-statistic to the critical F-value at the 0.05 significance level. If the calculated F is greater, reject the null hypothesis, indicating a significant difference in the number of rounds played by day of the week. If not, fail to reject the null hypothesis.