This problem is asking whether there is a significant difference in the average hourly wages across the three areas. Since we are comparing the means of three different groups (Area 1, Area 2, and Area 3), we can use ANOVA (Analysis of Variance) to test for significant differences among the means of the groups.

Steps:

1. Null Hypothesis ($H_0$): The average hourly wages in the three areas are the same (i.e., $\mu_1 = \mu_2 = \mu_3$).
2. Alternative Hypothesis ($H_A$): At least one of the areas has a different average hourly wage.

Given Data:

• Area 1: 19, 17, 21, 14, 18, 25, 22, 17
• Area 2: 24, 25, 18, 15, 23, 23, 16, 17
• Area 3: 11, 9, 16, 25, 11, 15, 10, 21

Steps for calculating ANOVA:

1. Calculate the grand mean (overall average wage).
2. Compute the sum of squares for treatment (SST) — this measures the variation between the group means.
3. Compute the sum of squares for error (SSE) — this measures the variation within the groups.
4. Calculate the mean square for treatment (MST) and mean square for error (MSE).
5. Finally, compute the F-statistic: $F = \frac{\text{MST}}{\text{MSE}}$
6. Compare the computed F-statistic to the critical value from the F-distribution table or use a p-value to determine significance.

Let me calculate these values for you.The value of the test statistic (F-statistic) is approximately 3.23.

This F-value can be compared to the critical value from the F-distribution table for a given significance level (typically $\alpha = 0.05$) or used to compute the p-value to determine if the difference in the means is statistically significant.

Would you like to proceed with calculating the p-value or have more details about the process?

Here are 5 related questions:

1. How do we interpret the F-statistic in ANOVA tests?
2. What is the significance of the p-value in ANOVA?
3. How do we check assumptions in an ANOVA test?
4. What are post-hoc tests, and when should they be used?
5. What happens if the assumptions of ANOVA are violated?

Tip: ANOVA assumes that the data in each group follows a normal distribution and that the variances across the groups are equal (homoscedasticity). Always check these assumptions before interpreting results.