Respuesta :
Answer:
Based on the provided data, we can analyze the manager's question using an ANOVA (Analysis of Variance) test to compare the means of the three industry groups. However, due to the small sample size (n = 5 in each group), it's important to proceed with caution and consider alternative tests.
Here's how we can approach the analysis:
1. Assumptions for ANOVA:
Before performing ANOVA, we need to check if the assumptions for the test are met:
Normality: Check if the data within each group and the overall data are normally distributed. You can use visual methods like histograms and normality tests like Shapiro-Wilk.
Homoscedasticity: Check if the variances of the three groups are equal. You can use Levene's test for equality of variances.
2. ANOVA Test:
If the assumptions are met, we can perform a one-way ANOVA test to compare the means of the three groups. This will provide an F-statistic and a p-value.
3. Alternative Tests:
If the assumptions are not met, we can consider alternative non-parametric tests that don't require normality or homoscedasticity. Two options, depending on the data distribution, are:
Kruskal-Wallis test: for non-normal data.
Welch's ANOVA: for unequal variances.
4. Interpretation:
Once we have the F-statistic and p-value (or the equivalent for the alternative test), we can interpret the results at the 0.05 significance level:
If the p-value < 0.05: We reject the null hypothesis of no difference and conclude that there is statistically significant evidence of a difference in the mean hours spent per week between the three industries.
If the p-value >= 0.05: We fail to reject the null hypothesis and cannot conclude that there is a statistically significant difference between the groups.
5. Limitations:
Remember that with such a small sample size, the results might be less reliable or generalizable. Consider increasing the sample size for a more conclusive analysis.
