This Week You Will Begin Working On Phase 3 Of Your Course

This Week You Will Begin Working On Phase 3 Of Your Course Project Us

This week you will begin working on Phase 3 of your course project. 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. Submit your completed assignment to the drop box below.

Please check the Course Calendar for specific due dates. Save your assignment as a Microsoft Word document. (Mac users, please remember to append the ".docx" extension to the filename.) The name of the file should be your first initial and last name, followed by an underscore and the name of the assignment, and an underscore and the date. An example is shown below:

Paper For Above instruction

The process of hypothesis testing is fundamental to inferential statistics, enabling researchers to make data-driven decisions about population parameters based on sample data. This procedure involves a systematic approach that ensures objectivity and rigor in evaluating claims or hypotheses about population characteristics. The eight essential steps of hypothesis testing include: (1) State the null and alternative hypotheses, (2) Choose the significance level (α), (3) Identify the appropriate test statistic, (4) Determine the sampling distribution of the test statistic, (5) Calculate the test statistic value, (6) Find the P-value or critical value, (7) Make a decision to reject or fail to reject the null hypothesis, and (8) State the conclusion in practical terms.

Among the two primary methods for hypothesis testing—the P-value method and the critical value method—I favor the P-value approach for its flexibility and clarity. The P-value provides a precise measure of evidence against the null hypothesis, allowing decision-makers to interpret results in a more nuanced manner. Conversely, the critical value method relies on fixed thresholds, which can sometimes oversimplify the interpretation. The P-value method also facilitates the comparison of results across different significance levels, offering greater adaptability.

Suppose the hypothesis test concerns the claim that the average salary for all jobs in Minnesota is less than $65,000 (Option 1). The null and alternative hypotheses are:

Null hypothesis (H₀): μ ≥ 65,000

Alternative hypothesis (H₁): μ

This is a one-tailed test because the claim is directional, testing whether the mean salary is less than the specified value. The test is left-tailed, as the critical region is on the lower end of the sampling distribution.

Given that the population standard deviation (σ) is unknown and the sample size is typically small or moderate, a Student’s t-test is appropriate. The t-test compares the sample mean to the hypothesized population mean while accounting for sample variability.

Let's assume, based on data, we have the sample mean (x̄), sample standard deviation (s), and sample size (n). The test statistic is calculated as:

t = (x̄ - μ₀) / (s / √n)

where μ₀ = 65,000 in this case. The degrees of freedom (df) would be n - 1. Using the calculated t-value, we determine the P-value by referencing the t-distribution table or software. The critical value for α = 0.05 and df = n - 1 is obtained similarly.

If, for example, the test statistic t equals -2.10, the P-value for a left-tailed test might be approximately 0.023. If the critical value at α = 0.05 is approximately -1.699 (for df = n - 1), since our t-value is beyond the critical value (more negative), we reject the null hypothesis. Conversely, if the P-value is less than α, we also reject H₀. If not, we fail to reject H₀.

The decision-making process involves comparing the P-value to α and the test statistic to the critical value. In either case, a result indicating sufficient evidence to suggest that the average salary is less than $65,000 leads us to reject the null hypothesis. Otherwise, we do not reject H₀.

The conclusion in non-technical terms: Based on the data, there is statistically significant evidence at the 5% level to support the claim that the average salary for all jobs in Minnesota is less than $65,000. This suggests that the average salary has likely decreased below the specified threshold, which could impact workforce planning and policy decisions.

In conducting this hypothesis test, the construction of the test statistic involved calculating the difference between the sample mean and the hypothesized population mean, scaled by the standard error. The P-value was obtained through software or t-distribution tables, providing the probability of observing such a test statistic under the null hypothesis. The critical value was similarly derived based on the significance level and degrees of freedom, establishing the threshold for decision-making.

References

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