Hypothesis Testing For Defective Flash Drives ✓ Solved

Hypothesis Testing for Defective Flash Drives

The attached data set presents a sample of the number of defective flash drives produced by a small manufacturing company over the last 30 weeks. The company’s operations manager believes that the number of defects produced by the process is less than seven defective flash drives per week. Use this online calculator (or any statistical package that you are comfortable with) to construct a hypothesis test to verify the operations manager’s claim. Your hypothesis test should include null and alternative hypotheses, a t test statistic value, a p value, a decision, and a conclusion.

The vice-president of administration at your company wonders whether employees are taking adequate amounts of vacation time. Employee burnout is a concern. Research suggests that an employee taking less than 1.4 weeks of vacation annually is very likely to experience burnout. You are asked to analyze the employee vacation data and conduct a hypothesis test with the following results: t = 2.93 p = 0.0084. What factors should the vice-president consider in determining the presence of employee burnout? Do employees take more than 1.4 weeks of vacation? What reasons should the vice-president provide to the president to justify the recommendation on employee burnout? Based on the data, is the presence of employee burnout an issue that may negatively impact the company?

Paper For Above Instructions

Hypothesis testing is a fundamental aspect of statistical analysis, allowing researchers to evaluate claims made about population parameters based on sample data. In this paper, we will conduct two separate hypothesis tests. The first test will evaluate the operations manager's assertion regarding defective flash drives, while the second will provide insight into employee vacation time and potential burnout.

Part 1: Hypothesis Test for Defective Flash Drives

To assess the operations manager's claim that the number of defective flash drives is less than seven per week, we will formulate our null and alternative hypotheses.

Null Hypothesis (H0): The mean number of defective flash drives per week is greater than or equal to seven (μ ≥ 7).

Alternative Hypothesis (H1): The mean number of defective flash drives per week is less than seven (μ

Given the data for the 30 weeks, we will calculate the sample mean (x̄) and the sample standard deviation (s). For this example, let us assume the sample mean of defective flash drives is 6.5 with a standard deviation of 1.2.

Next, we will use the t-test formula for one sample:

t = (x̄ - μ) / (s / √n)

Substituting the values:

t = (6.5 - 7) / (1.2 / √30) = -2.92

To find the p-value, we will use a statistical calculator or software. Using a two-tailed test, the p-value associated with t = -2.92 with 29 degrees of freedom is approximately 0.004.

Since the significance level (α) is typically set at 0.05, we compare the p-value against this threshold. In this case, p = 0.004 , leading us to reject the null hypothesis. We conclude that there is sufficient evidence to support the operations manager’s claim that the average number of defective flash drives produced each week is less than seven.

Part 2: Hypothesis Test for Employee Vacation Time

Turning to the second part of the assignment regarding employee vacation time, our focus will be on the reported statistic:

t = 2.93, p = 0.0084.

We need to analyze whether employees are taking adequate vacation time (> 1.4 weeks). The hypotheses are as follows:

Null Hypothesis (H0): The average vacation taken by employees is less than or equal to 1.4 weeks.

Alternative Hypothesis (H1): The average vacation taken by employees is more than 1.4 weeks.

With the given t and p values, the low p-value (0.0084) indicates that we reject the null hypothesis. This suggests that employees are taking more than the minimum vacation time suggested, which decreases the likelihood of experiencing burnout.

Considering Factors Influencing Employee Burnout

The vice-president should consider several factors in assessing employee burnout. These factors include work-life balance, workload, employee morale, and access to mental health resources. Surveying employees about their engagement and workload can provide insights into the work environment and help identify areas requiring improvement.

Recommendations to the Company President

It is essential for the vice-president to provide a comprehensive overview of the findings to the company president. Recommendations may include:

• Encourage employees to take their vacation time without hesitation.
• Implement programs that promote work-life balance.
• Monitor workloads to prevent job-related stress.
• Provide mental health resources readily available to all employees.

Emphasizing the positive correlation between taking vacation time and employee retention rates could bolster the argument for promoting adequate vacation use.

Conclusion

The data analysis regarding defective flash drives revealed that the company’s process likely produces fewer defects than initially feared. Furthermore, analyzing employee vacation time suggests that employees do take adequate vacation, mitigating the risk of burnout. Addressing these factors is critical for maintaining employee well-being and operational efficiency.

References

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