Question

Chapin Manufacturing Company operates 24 hours a day, five days a week. The workers rotate shifts each week. Management is interested in whether there is a difference in the number of units produced when the employees work on various shifts. A sample of five workers is selected and their output recorded on each shift. At the 0.05 significance level, can we conclude there is a difference in the mean production rate by shift or by employee? Units Produced Employee Day Afternoon Night Skaff 36 22 35 Lum 38 26 34 Clark 25 26 38 Treece 37 29 25 Morgan 25 25 33

Answer 1

To address whether there is a difference in production rates by shift or employee at Chapin Manufacturing Company, a two-way ANOVA test can be used. This will ascertain if the mean production rate differs across shifts and employees, by comparing the calculated p-values against the significance level of 0.05.

Step-by-step explanation:

To determine whether there is a significant difference in the mean production rate by shift or by employee at Chapin Manufacturing Company, we can utilize a two-way ANOVA (Analysis of Variance). This statistical test is appropriate when comparing the means of three or more independent groups (in this case, the different shifts) and to see if there is an interaction between two factors (shifts and employees).

To perform a two-way ANOVA, we must first set up the null hypothesis for shifts (H0: μ1 = μ2 = μ3, where μ represents the mean units produced in different shifts) and for employees (H0: no difference in mean production rate by employee). Similarly, the alternative hypothesis would suggest that there is a significant difference in at least one of the means.

After calculating the ANOVA table, F-values and p-values for both factors and their interaction, if the p-value is less than the significance level (α = 0.05), we reject the null hypothesis and conclude that there is a significant difference. If it's greater, we fail to reject the null hypothesis.