Deliverable 4: Hypothesis Tests Competency Given A Real-Life

Deliverable 4 Hypothesis Testscompetencygiven A Real Life Applicatio

Scenario (information repeated for deliverable 01, 03, and 04): A major client of your company is interested in the salary distributions of jobs in the state of Minnesota that range from $30,000 to $200,000 per year. As a Business Analyst, your boss asks you to research and analyze the salary distributions. You are given a spreadsheet that contains the following information: A listing of the jobs by title and the salary (in dollars) for each job. The dataset from the Bureau of Labor Statistics includes 364 records with job titles and annual salaries ranging approximately from $30,000 to $200,000 for Minnesota. Your task is to develop and interpret hypothesis tests concerning the population mean salary, specifically testing the claims that the average salary is less than $74,500 and greater than $70,500. Your boss requires a comprehensive explanation of all steps involved in hypothesis testing, including hypothesis formulation, test statistic calculation, critical value determination, decision-making criteria, p-value interpretation, and final conclusions.

Specifically, you need to:

1. Explain the 8 steps in hypothesis testing process.
2. Describe the decision criteria for rejecting the null hypothesis using both the p-value method and the critical value method.
3. Formulate null and alternative hypotheses for the claims concerning the population mean salary in Minnesota.
4. Select and compute the appropriate test statistic (z or t), providing calculations and justification.
5. Determine the critical value(s) for the test, define the rejection region, and explain their significance.
6. Make a decision using the critical value approach, interpret it in non-technical terms, and conclude about the claim.
7. Calculate the p-value, interpret it, and compare it with the critical value method for consistency in decision-making.
8. Provide the completed spreadsheet with all calculations, answers, and detailed analysis supporting your conclusions.

Paper For Above instruction

Hypothesis testing is a fundamental statistical method used to make inferences about a population parameter based on sample data. The process involves several systematic steps designed to assess the validity of a specific claim, known as the alternative hypothesis, against a null hypothesis that represents the status quo or a position of no effect or difference. Analyzing the salary data for Minnesota's jobs demonstrates the application of these steps in real-world decision-making and highlights important concepts such as test statistics, significance levels, critical values, and p-values.

Step 1: State the hypotheses

The initial step involves formulating null and alternative hypotheses. For the claims under consideration, the null hypothesis (H0) assumes that the mean salary μ equals a specific value, while the alternative hypotheses (Ha) suggest a deviation from this value. For the claim that the average salary is less than $74,500, the hypotheses are:

• H0: μ ≥ $74,500
• Ha: μ

Similarly, for the claim that the average salary exceeds $70,500, the hypotheses are:

• H0: μ ≤ $70,500
• Ha: μ > $70,500

These hypotheses are directional, leading to one-tailed tests. The hypotheses are clearly claims about the population mean based on the salary data.

Step 2: Choose the significance level and select the test

The significance level (α) represents the probability of rejecting the null hypothesis when it is true. Commonly set at 0.05, it guides the threshold for statistical significance. Given the large sample size (n=364), the z-test is typically appropriate due to the Central Limit Theorem applying to sample means, provided the population standard deviation is known or the sample standard deviation is sufficiently accurate.

Step 3: Calculate the test statistic

The test statistic quantifies how far the sample mean deviates from the hypothesized population mean under the null hypothesis, standardized by the variability in the data. The formula for the z-test statistic is:

z = (x̄ - μ₀) / (s / √n)

where x̄ is the sample mean, μ₀ is the hypothesized mean, s is the sample standard deviation, and n is the sample size. Using the sample data, calculations yield the specific test statistic value, which indicates the number of standard errors that the sample mean is away from the hypothesized mean.

Step 4: Determine the critical value(s) and rejection region

Critical values depend on the significance level and the type of test. For a left-tailed test at α = 0.05, the critical z-value is approximately -1.645; for a right-tailed test at the same significance level, it is +1.645. For a two-tailed test, the critical z-values are ±1.96. Since we are testing claims like "less than" or "greater than," one-tailed tests are appropriate. The rejection region consists of all values of the test statistic that fall beyond the critical value in the tail.

Step 5: Make a decision using the critical value approach

Compare the computed test statistic to the critical value. If the test statistic falls into the rejection region (e.g., less than -1.645 for the first claim or greater than 1.645 for the second), reject the null hypothesis. Otherwise, do not reject it. The decision is then interpreted in plain language: for example, "There is sufficient evidence to conclude that the average salary is less than $74,500" or "Insufficient evidence exists to support the claim that the average salary exceeds $70,500."

Step 6: Calculate the p-value and interpret it

The p-value measures the probability of observing the sample data, or something more extreme, if the null hypothesis is true. It provides an alternative way to make the rejection decision: reject H0 if the p-value is less than α, and do not reject if it is greater. Comparing the p-value to the significance level offers a nuanced understanding of the evidence against the null hypothesis.

Step 7: Draw conclusions and report

Both the decision based on the critical value and the p-value should be consistent. If both methods lead to rejecting or not rejecting the null hypothesis, the conclusion is robust.

For example, if the calculated p-value for the first claim is less than 0.05, the conclusion supports the claim that the average salary is less than $74,500, otherwise not. Summarizing these findings provides clarity for the client regarding the salary distribution in Minnesota.

Step 8: Submit complete analysis

The final step is to compile all calculations, test results, interpretations, and conclusions into a comprehensive report. This includes the spreadsheet with all formulas, the reasoning behind each step, and a clear narrative explaining the statistical evidence regarding the salary claims.

Conclusion

Hypothesis testing offers a structured framework for making data-driven decisions about population parameters. Applied to salary data in Minnesota, this process enables analysts to rigorously evaluate claims, providing clients with validated insights. Both the p-value and critical value approaches serve as valuable tools, and their consistent use ensures the reliability of the conclusions drawn from the analysis. Ultimately, transparent and thorough hypotheses testing supports effective decision-making in business contexts, informing strategies and policies linked to the salary data.

References

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