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	 	120	 
Tuesday	 	145	 
Wednesday	 	140	 
Thursday	 	110	 
Friday	 	110	 
 
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.
 
a. State the decision rule, using the 0.01 significance level. (Round your answer to 3 decimal places.)

We are testing whether there is a difference in the number of rounds of golf played per weekday at the five golf courses. We can approach this problem by performing a **One-Way ANOVA** (Analysis of Variance), since we are comparing the means of rounds played across more than two groups (days of the week).

### Hypotheses:
- **Null hypothesis (H₀)**: The mean number of rounds played is the same for each day of the week.
- **Alternative hypothesis (H₁)**: The mean number of rounds played is not the same for each day of the week.

### Significance Level:
- **α = 0.01** (1%)

### Steps for the One-Way ANOVA Test:
1. **Calculate the grand mean** (the mean of all rounds played).
2. **Compute the sum of squares** between groups (SSB) and within groups (SSW).
3. **Calculate the F-ratio**: \( F = \frac{\text{Mean Square Between}}{\text{Mean Square Within}} \)
   - Mean Square Between (MSB) = SSB / (k - 1), where \(k\) is the number of groups (days of the week).
   - Mean Square Within (MSW) = SSW / (N - k), where \(N\) is the total number of data points.
4. **Determine the critical F-value** from the F-distribution table at \( \alpha = 0.01 \), with degrees of freedom:
   - df₁ = \(k - 1\) (numerator, between groups)
   - df₂ = \(N - k\) (denominator, within groups)
5. **Decision rule**: If the calculated F-ratio is greater than the critical F-value, reject the null hypothesis.

### Let's compute each step:

**Data:**
- Monday: 120 rounds
- Tuesday: 145 rounds
- Wednesday: 140 rounds
- Thursday: 110 rounds
- Friday: 110 rounds

We'll calculate the necessary values and determine the decision rule. Let me compute it for you.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, you can still follow the steps I outlined earlier to perform the calculations manually or using a statistical software package to complete the analysis.

If you have further questions or need help with specific steps, feel free to ask!

Here are 5 related questions you can consider:
1. How is the F-ratio interpreted in ANOVA?
2. What happens if the significance level is changed from 0.01 to 0.05?
3. How would you test differences in rounds if there were more than one value per day?
4. What are some assumptions of the One-Way ANOVA?
5. How do you calculate the sum of squares in ANOVA?

**Tip**: Always verify ANOVA assumptions, like normality and homogeneity of variance, before relying on results.

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: Monday - 120, Tuesday - 145, Wednesday - 140, Thursday - 110, Friday - 110. 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. a. State the decision rule, using the 0.01 significance level. (Round your answer to 3 decimal places.)

Analyze the difference in the number of golf rounds played per weekday at Classic Golf Inc. using One-Way ANOVA. The problem includes key statistics concepts like hypothesis testing and the F-ratio formula. Data includes rounds played on Monday (120), Tuesday (145), Wednesday (140), Thursday (110), and Friday (110).

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