A 35-year-old man has been experiencing increased stress due to a demanding job and personal issues. He reports feeling fatigued, irritable, and has noticed that he is gaining weight around his abdomen. His blood sugar levels have also been consistently elevated. Based on his symptoms, what role is cortisol likely playing in his condition?

In summer 2023, the average house price for townhouses in State College was $285,000. A real estate agent believes that the mean price of townhouses in State College in summer 2024 has increased from the previous summer. Correct null and alternative hypothesis to answer this question is:   

A test for hypotheses

A company would like to see if the percentage of job satisfaction among their employees exceeds 45%. In a random sample of 36 employees, 19 said that they are satisfied with their job.  Based on the provided information, the point estimate for the true proportion employees in the company who are satisfied with their job is

For each situation provided below, select if the value mentioned in the statement is a parameter or a statistic.  The head of the statistics department is interested in knowing the ratio of the Statistics vs. Data Science pre-majors among the undergraduates in Fall 2024 intake. Of all the undergraduates accepted in FA 24, the ratio of the Statistics to Data Science pre-majors is 18:14. The value 18:14 is a [select1] Admissions office at Penn State World Campus is interested in getting an idea about the percentage of self-funded students who are enrolled in World Campus. In a random sample of 100 students, 45% said they are self-funded.  In this study, 45% is a [select2].

Please note that this question consists of six parts. You may use MINITAB to find a final answer. However you MUST show all the mathematical work to get to the final answer. Just giving the answer without adequate work/explanation may result in zero for the question.  A social scientist believes that the mean number of people per household has decreased. He is interested in testing if the true mean number of people per household is less than 2.8.  To test his hypothesis, he collected data from a random sample of 36 households and found that the sample mean number of people per household to be 2.2 with the sample standard deviation 1.25. Set up the appropriate null and alternative hypotheses for testing the scientist’s question.  Is/are the condition(s) to carry out the above test satisfied? In addition to answering yes or no, clearly state the condition(s) and explain how you check.   Calculate the test statistic. Show your calculations.  Find the rejection region for the test defined in part 1 using 5% significance level. Clearly state the rejection region (it is not sufficient to provide just the critical value). Write the final conclusion in the context of the problem.  Based on the decision you made in part 5, which error (type I or type II) is possible? Explain.   

In a large university, the administration is planing on increasing the student fees with the intention of using majority of the funds towards renovations in the football stadium. Administration wishes to estimate the true proportion of students who support the idea. How many students should be sampled if the administration wants to be 99% confident with a margin of error no more than 5%. 

When you host a mediation, who needs to sign a confidentiality form?  When do they need to sign it?  

During the mediation, parties are allowed to take photos of the board/chart notes 

How does a representative of a large business view mediation, compared to an individual (or the owner of a small business)?   How might that impact the mediator you select?