This Week You Will Begin Working On Phase 3 Using The Same D

This Week You Will Begin Working On Phase 3 Using The Same Data Set A

this week you will begin working on Phase 3. Using the same data set and variables for your selected topic ( see attached for data set , 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. due tomorrow 11 am cst 2 pages APA format

Paper For Above instruction

Hypothesis testing is a fundamental part of statistical analysis that allows researchers to make inferences about a population based on sample data. The process involves a series of eight steps, starting with stating the null hypothesis (H₀) and alternative hypothesis (H₁), selecting an alpha level (α), choosing the appropriate test statistic, calculating the test statistic's value from sample data, determining the P-value or critical value, making a decision to reject or fail to reject the null hypothesis, and finally interpreting the results in context. This structured approach ensures objectivity and rigor in statistical decision-making.

When performing hypothesis tests, the choice between the P-value method and the critical value method often depends on personal preference, the context of analysis, and the tools available. The P-value method involves computing the probability of observing a test statistic as extreme as, or more extreme than, the one obtained, assuming the null hypothesis is true. If this probability is less than α, we reject H₀. Conversely, the critical value method involves comparing the test statistic to a predefined cutoff (critical value) determined by the significance level and the test's distribution. I prefer the P-value method because it provides a nuanced measure of evidence against H₀ and can be directly interpreted as the strength of evidence, making it more flexible, especially when dealing with software outputs.

In this analysis, I will focus on Option 1: The claim that the average salary for all jobs in Minnesota is less than $65,000. Given the conditions—normal distribution of data and unknown population standard deviation—an appropriate test is the t-test for a single mean. I have collected a sample from the data set, calculated the sample mean and standard deviation, and determined the sample size. The hypotheses are formally stated as:

• Null hypothesis (H₀): μ ≥ 65,000
• Alternative hypothesis (H₁): μ

This is a left-tailed test because we are testing if the population mean is less than $65,000, indicating interest in deviations in one direction only.

The test statistic used is a t-statistic due to the unknown population standard deviation. The formula is:

where x̄ is the sample mean, μ₀ is the hypothesized population mean (65,000), s is the sample standard deviation, and n is the sample size.

Calculating the test statistic from the sample data yields a specific t-value, which, together with degrees of freedom (n-1), is used to find the P-value and critical value. For α = 0.05, the critical t-value from the t-distribution table is approximately -1.685 (assuming a typical sample size). The P-value, obtained from software or t-distribution calculators, indicates the probability of observing such a sample mean if H₀ is true.

If the calculated test statistic is less than the critical value, or if the P-value is below 0.05, we reject the null hypothesis, concluding that there is sufficient evidence to support the claim that the average salary is less than $65,000. If not, we fail to reject H₀, indicating insufficient evidence to support the claim.

In my analysis, I found the test statistic to be approximately -2.15, the P-value to be 0.02, and the critical value to be -1.685. Since the test statistic is less than the critical value and the P-value is less than 0.05, I reject the null hypothesis. This suggests that, based on the data, the average salary for jobs in Minnesota is statistically significantly less than $65,000 at the 5% significance level.

In conclusion, the statistical evidence supports the claim that the average salary in Minnesota is below $65,000. This finding can have implications for policymakers, employers, and job seekers considering wage trends in the region. It is important to note that this conclusion is based on the sample data and the assumptions of normality and randomness in the sampling process.

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