Using The Same Data Set And Variables For Your Topic

Using the same data set and variables for your selected topic add the

Using the same data set and variables for your selected topic, add the following information to your analysis: Discuss the process for hypothesis testing. Discuss the 8 steps of hypothesis testing? When performing the 8 steps for hypothesis testing, which method do you prefer; P-Value method or Critical Value method? Why? Perform the hypothesis test.

If you selected Option 1 : Original Claim : The average salary for all jobs in Minnesota is less than $65,000. Test the claim using α = 0.05 and assume your data is normally distributed and σ is unknown. If you selected Option 2: Original Claim : The average age of all patients admitted to the hospital with infectious diseases is less than 65 years of age. Test the claim using α = 0.05 and assume your data is normally distributed and σ is unknown. Based on your selected topic, answer the following: Write the null and alternative hypothesis symbolically and identify which hypothesis is the claim.

Is the test two-tailed, left-tailed, or right-tailed? Explain. Which test statistic will you use for your hypothesis test; z-test or t-test? Explain. What is the value of the test-statistic?

What is the P-value? What is the critical value? What is your decision; reject the null or do not reject the null? Explain why you made your decision including the results for your p-value and the critical value. State the final conclusion in non-technical terms.

Please show your work for the construction of the test-statistic and explain your process for finding the p-value and critical value. Be sure to use the Equation Editor to format your equations. This assignment should be formatted using APA guidelines and a minimum of 2 pages in length.

Paper For Above instruction

Hypothesis testing is a fundamental statistical procedure used to make inferences or draw conclusions about a population parameter based on sample data. This process involves a series of systematic steps that guide researchers in evaluating claims about population means or proportions. In this paper, I will discuss the eight-step process of hypothesis testing, compare the P-value method and the critical value method, and perform an example hypothesis test based on the selected scenario concerning average salaries in Minnesota.

The eight steps of hypothesis testing are as follows: First, state the null hypothesis (H₀) and alternative hypothesis (H₁). Second, choose the appropriate significance level (α), commonly set at 0.05. Third, identify the correct test statistic based on data characteristics (z-test or t-test). Fourth, gather sample data and compute the test statistic. Fifth, determine the probability (P-value) associated with the test statistic or find the critical value(s). Sixth, compare the P-value to α or the test statistic to the critical value(s) to make a decision. Seventh, interpret the results in the context of the research question. Finally, conclude whether to reject or fail to reject the null hypothesis.

Between the P-value method and the critical value method, I prefer the P-value approach because it provides a direct measure of the strength of evidence against the null hypothesis, and it allows for easier interpretation when dealing with asymmetric hypotheses or multiple tests. The P-value indicates the probability of observing a test statistic as extreme or more extreme than the one calculated, assuming H₀ is true. If the P-value is less than α, we reject H₀, indicating the data provides statistically significant evidence against the null.

To illustrate this process, I will undertake the hypothesis test for Option 1: the claim that the average salary for all jobs in Minnesota is less than $65,000. Assume a sample size of 30, with a sample mean of $63,500 and a sample standard deviation of $4,500. Given the population standard deviation is unknown, a t-test is appropriate. The null and alternative hypotheses are:

• H₀: μ ≥ $65,000 (the mean salary is greater than or equal to $65,000)
• H₁: μ

This is a left-tailed test because we are testing whether the population mean is less than the specified value. The test statistic is calculated using the t-formula:

t = (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. Substituting the given data:

t = (63,500 - 65,000) / (4,500 / √30) ≈ -1.87

Using a t-distribution table or statistical software, the P-value corresponding to t = -1.87 with 29 degrees of freedom is approximately 0.035. The critical t-value for a one-tailed test at α = 0.05 and df = 29 is approximately -1.701. Since the calculated t-value (-1.87) is less than the critical value (-1.701), and the P-value (0.035) is less than α (0.05), we reject the null hypothesis.

This means there is sufficient evidence at the 5% significance level to support the claim that the average salary for jobs in Minnesota is less than $65,000. In practical terms, the data suggests the average salary is likely below $65,000.

In conclusion, the hypothesis test, taking into account the test statistic, P-value, and critical value, confirms the claim under the specified significance level. This systematic approach ensures the reliability of the inference and demonstrates the importance of hypothesis testing in statistical analysis.

References

• Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics. Sage Publications.
• Gibbons, J. D., & Chakraborti, S. (2011). Nonparametric Statistical Inference. CRC Press.
• Moore, D. S., McCabe, G. P., & Craig, B. A. (2012). Introduction to the Practice of Statistics. W.H. Freeman.
• Rumsey, D. J. (2016). Statistics for Dummies. Wiley.
• Walpole, R. E., Myers, R. H., Myers, S. L., & Ye, K. (2012). Probability & Statistics for Engineering and the Sciences. Pearson.
• McClave, J. T., & Sincich, T. (2018). Statistics (12th ed.). Pearson.
• Ott, R. L., & Longnecker, M. (2015). An Introduction to Statistical Methods and Data Analysis. Cengage Learning.
• Levine, D. M., Stephan, D. F., Krehbiel, T. C., & Berenson, M. L. (2018). Statistics for Managers Using Microsoft Excel. Pearson.
• Altman, D. G. (1991). Practical statistics for medical research. Chapman and Hall/CRC.
• Newbold, P., Carlson, W. L., & Thorne, B. (2013). Statistics for Business and Economics. Pearson.