Question Set 1: Proportion of Employees Who Own Their Homes

In this question set you will be working with the following scenario. A very large company is interested in learning more about its employees' current housing situations. In a random sample of 100 employees, 55 owned their home. Use these sample data to answer the following questions.

A. Use the five-step hypothesis testing procedure outlined below to determine if there is evidence that the proportion of all employees who own their home is different from 0.5 (i.e., is the population proportion different from 0.5?). Use Minitab Express. If assumptions are met, use the normal approximation method. Other than checking assumptions, No calculations by hand needed. Remember to include all relevant Minitab Express output and to clearly identify your answers to each step. [25 points]

Step 1: Check assumptions and write hypotheses

Step 2: Calculate the test statistic

Step 3: Determine the p value

Step 4: Decide to reject or fail to reject the null

Step 5: State a "real world" conclusion

B. Construct a 95% confidence interval to estimate the proportion of all employees at this company who own their homes. Show how you checked assumptions. If assumptions were met, use the normal approximation method. Remember to include all relevant Minitab Express output and to clearly identify your answer. No calculations by hand needed. [15 points]

C. What sample size would be needed to construct a 95% confidence interval to estimate the proportion of all employees who own their home with a margin of error of 2%? Use the observed sample proportion from the scenario as an estimate for the population proportion. Calculations by hand needed. Show all of your work using the equation editor. [10 points]

Question Set 2: Mean Monthly Rent

A researcher is studying the cost-of-living in a city. As part of their research, they would like to learn more about the average monthly rental rate of two-bedroom apartments in this area. In a random sample of 40 apartments in the area, the mean monthly rental rate was $1452.23 with a standard deviation of $481.19. Use these sample data to answer the following questions.

A. Use the five-step hypothesis testing procedure outlined below to determine if there is evidence that the mean monthly rental rate of all two-bedroom apartments in this area is different from $1800. Use Minitab Express to conduct a single sample mean t test. No calculations by hand needed. Remember to include all relevant Minitab Express output and to clearly identify your answers to each step. [25 points]

Step 1: Check assumptions and write hypotheses

Step 2: Calculate the test statistic

Step 3: Determine the p value

Step 4: Decide to reject or fail to reject the null

Step 5: State a "real world" conclusion

B. Construct a 95% confidence interval to estimate the mean monthly rental rate of all two-bedroom apartments in this area. Remember to include all relevant Minitab Express output and to clearly identify your answer. No calculations by hand necessary. [15 points]

C. What sample size would be needed to construct a 95% confidence interval to estimate the mean monthly rental rate of all two-bedroom apartments in this area with a margin of error of $50? Calculations by hand needed. Show all of your work using the equation editor. [10 points]