BUSINESS-SYM-506 Grand Canyon University – The human resources director is studying the age of employees at two different plants (A and B).

QUESTION

The human resources director is studying the age of employees at two different plants (A and B). The director wants to test to see if there is a difference in the average ages of the employees at the two plants. If he obtained a z-value of 1.88, what decision should be made? Assume α=0.05.

ANSWER

 Analyzing the Difference in Average Ages of Employees at Plants A and B

Introduction

In this study, the Human Resources Director is investigating whether there is a significant difference in the average ages of employees at two different plants, Plant A and Plant B. By conducting a hypothesis test, the director aims to determine if there is sufficient evidence to conclude that the average ages of employees at the two plants are different. The obtained z-value of 1.88 will serve as a critical indicator in making this decision, considering a significance level (α) of 0.05.

Hypothesis Testing

To conduct the hypothesis test, the director needs to establish the null and alternative hypotheses based on the research question. The null hypothesis (H0) assumes that there is no difference in the average ages of employees at Plants A and B, while the alternative hypothesis (Ha) posits that there is a significant difference.

H0: μA = μB (There is no difference in the average ages of employees at Plants A and B)

Ha: μA ≠ μB (There is a significant difference in the average ages of employees at Plants A and B)

The obtained z-value of 1.88 represents the test statistic derived from the sample data. This value measures the number of standard deviations that the sample mean differs from the hypothesized population mean under the null hypothesis.

Decision Making

To determine the decision, the director needs to compare the obtained z-value with the critical value(s) corresponding to the chosen significance level (α = 0.05). The critical value is obtained from the standard normal distribution table or statistical software.

For a two-tailed test at α = 0.05, the critical z-values are approximately -1.96 and 1.96. If the obtained z-value falls within this range, it suggests that the sample mean is within the range of expected values under the null hypothesis. On the other hand, if the obtained z-value is beyond this range, it indicates that the sample mean deviates significantly from the expected values, leading to the rejection of the null hypothesis.

Considering the obtained z-value of 1.88, which falls outside the critical range of -1.96 to 1.96, we can conclude that there is sufficient evidence to reject the null hypothesis. This means that there is a significant difference in the average ages of employees at Plants A and B.

Conclusion

Based on the obtained z-value of 1.88 and a significance level of α = 0.05, the decision is to reject the null hypothesis. This suggests that there is a significant difference in the average ages of employees at Plants A and B. The findings from this statistical analysis provide valuable insights to the Human Resources Director, enabling them to make informed decisions related to workforce planning, employee engagement, and talent management at the two plants.

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