Hypothesis Tests

1.       Describe the 8 steps in the process for hypothesis testing. Explain the decision criteria for rejecting the null hypothesis for both the p-value method and the critical value method.

Answer and Explanation:

The remaining problems refer to the following scenario:

A claim is made that the average salary for all jobs in Minnesota is less than $65,000.  You are going to test the claim using and assume that your data is normally distributed and the population standard deviation  is not known.

2.       Write the null and alternative hypotheses symbolically and identify which hypothesis is the claim.  Then identify if the test is left-tailed, right-tailed, or two-tailed and explain why.

Answer and Explanation:

3.       Identify and explain which test statistic you will use for your hypothesis test: z or t?  Find the value of the test statistic.

Answer and Explanation:

4.       What is the critical value?  Describe the rejection region.

Answer and Explanation:

5.       Using the critical value approach, should you reject the null hypothesis or not reject the null hypothesis?  Explain. After making your decision, restate it in non-technical terms and make a conclusion about the original claim.

Answer and Explanation:

The value of the calculated t value is -2.6840. This value falls outside the acceptance region. So we reject the null hypothesis at 0.05 level of significance. In other words, there is enough evidence to support the claim that the average salary for all jobs in Minnesota is less than $65,000.

6.       Calculate the p-value for this hypothesis test, and state the hypothesis conclusion based on the p-value.  Does this match your results from the critical value method?

Answer and Explanation:

  

The P-value of the t score can be calculated using a statistic software or p-value calculator. In this case, we obtain the p-value of the test score t=-2.6840 as 0.003804 (Soper, 2017) . Since p<α, we reject the null hypothesis and conclude that there is enough evidence to support the claim that the average salary for all jobs in Minnesota is less than $65,000.

 

References

LaMorte, W. W. (2017, November 6). Hypothesis Testing for Means and Proportions. Retrieved from Boston University School of Public Health: http://sphweb.bumc.bu.edu/otlt/mph-modules/bs/bs704_hypothesistest-means-proportions3.html

Soper, D. (2017, December 1). Free Statistics Calculators. Retrieved from Free Statistics Calculator: https://www.danielsoper.com/statcalc/default.aspx