Hypothesis Testing – The Mean Salary for Engineering Managers at XYZ Company

Hypothesis Testing – The Mean Salary for Engineering Managers at XYZ Company

In order to test the claim that the mean salary for engineering managers at XYZ Company is at least $170,000, a one-tailed hypothesis test with a significance level of 0.05 was conducted. The null hypothesis (H0) and alternative hypothesis (Ha) are the following.

• Null Hypothesis (H₀): The mean salary for engineering managers at XYZ Company (μ (mu)) is greater than or equal to $170,000.
  • H₀: mu >= $170,000
• Alternative Hypothesis (H_a): The mean salary for engineering managers at XYZ Company (μ) is less than $170,000.
  • H_a: mu < $170,000

Next, it was essential to find the sample mean salary for engineering managers in the company. From the provided data, the sample mean salary is:

• Sample Mean Salary = $174,339

Next, the confidence interval to test the claim was calculated. Since we conducted a one-tailed test with a significance level of 0.05, we had to find the critical value corresponding to this significance level. For a one-tailed test, one looks for the z-value that leaves 5% of the data in the tail (95% confidence level). Consulting the standard normal distribution table, the critical z-value is approximately -1.645.

The confidence interval was constructed as follows:

• CI = Sample Mean ± (Critical Value) * (Standard Error)

The standard error can be calculated as follows:

• Standard error = Standard Deviation / √Sample Size (Zach, 2022)

From the given data related to employee salaries:

• Standard Deviation = $95,378
• Sample Size, n = 225
• Standard Error = $95,377.67 / √225 ≈ $6,352.59

Now, we can calculate the confidence interval as follows:

• CI = $174,338.75 ± (-1.645) * $6,352.59

Therefore,

• CI ≈ $174,338.75 – $10,457 to $174,339

As the calculated confidence interval includes only positive values, we fail to reject the null hypothesis. There is not enough evidence to suggest that the mean salary for engineering managers at XYZ Company is less than $170,000. Therefore, based on the data and the hypothesis test, one can conclude that, with 95% confidence, the mean salary for engineering managers at XYZ Company is at least $170,000.

Therefore, the leadership’s claim that the mean salary for engineering managers is at least $170,000 is supported by the data, and there is no significant evidence to suggest otherwise. XYZ Company’s engineering managers’ salaries appear to be on par with industry standards, which aligns with the company’s goal to treat its employees well and remain competitive in the post-pandemic climate.

References

Zach. (2022). Standard deviation vs. standard error: What’s the difference? Statology. https://www.statology.org/standard-deviation-vs-standard-error/

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The recent pandemic greatly affected the working environment. According to a survey, post-pandemic employees are more than ever demanding changes to policies and benefits in the workplace.

Your organization, XYZ Company, notes several hurdles to attracting and retaining staff in the post-pandemic climate. One example is the employer’s inability to adjust to the remote work arrangement, and another is a lack of pay equity commitment.

In keeping with XYZ Company’s goal to treat employees well, management is looking for feedback to measure the company’s performance as the employer of choice.

You work as the Manager of Workforce Analytics within the Human Resources department. The company is growing rapidly, and your boss, Jane, who is the Chief People Officer (CPO), wants to make sure that the company is treating its employees equitably. She is analysis-driven, so she taps you to work on several projects to uncover any potential issues. Her objectives are to:

Describe the current state of salary data using the measures of central tendency and variability.
Give a point estimate and construct a confidence interval of the number of employees who want to work remotely.
Conduct a hypothesis test from two populations, male employees and female employees, of a claim that they have the same mean salary.
Test a claim that employee pay is on par with industry standards with a hypothesis test from one population.
Apply a normal distribution to review the current dental insurance plan expenses
Identify any correlation between seniority and pay
Conduct a regression analysis between employee age and salary
Let’s get started and gather insights into the workforce data.

Click the ‘scenario’ button below to review the topic and then answer the following question:

The leadership wants to ensure that the employee pay is on par with industry standards. For an engineering manager, the industry average is $170,000.

Using a 0.05 significance level, construct a confidence interval (round to dollar) to test the claim that for the engineering managers in the company, the mean salary is at least $170,000. State the null hypothesis and alternative hypothesis in symbolic form (use transliteration ‘mu’ in place of µ), and find the sample mean salary. Explain whether you reject or fail to reject the null hypothesis, and state a final conclusion that addresses the original claim.