[#1]Unknown population mean.

Suppose a company's legal department is concerned that an online web course on compliance training is taking too long for its employees to complete.They obtained a random sample of 90 employees who completed the online course.In the sample, the average employee needed 210 minutes to complete the online training course.Assume you do not know the actual population mean, but you do know that the population standard deviation is equal to 50 minutes.Using a significance level of 0.05, answer the questions below:

(a)Is there enough evidence to suggest that the average completion time exceeded 200 minutes?Conduct a hypothesis using the test statistic method and interpret your result.

(b)Re-do part (a) using the p-value method.

(c)Is there enough evidence to suggest that the average completion time differed from 240 minutes?Conduct a hypothesis using the test statistic method and interpret your result.

(d)Re-do part (c) using the p-value method.

[#2]Regression results.

Suppose you work for an insurance company.A regression analysis predicting a person's age at death is shown below.The variables of the regression model include:

Y = Longevity = The age at death for a former policyholder.

X1 = Mother = The age at death for the former policyholder's mother.

X2 = Father = The age at death for the former policyholder's father.

a.In words, interpret the meaning of the y-intercept.

b.In words, interpret the meaning of the value of unstandardized slope coefficient on the Mother variable.More specifically, write down the value and explain what that specific value means.

c.Using the test statistic method, do a hypothesis test for whether a linear relationship exists between a policyholder's age at death and his/her father's age at death. Show all steps to your hypothesis test and use a significance level of 5%.

d.In words, interpret the R-square value.

[#3] Regression Results, Part 2

Suppose you work for the same insurance company.Now you obtained data on additional variables to include in your analysis.A regression model predicting a policyholder's age at death is shown above.The variables included in this new regression model are:

Y = Longevity = The age at death for a former policyholder.

X₁ = Mother = The age at death for the former policyholder's mother.

X₂ = Father = The age at death for the former policyholder's father.

X₃ = Smoker = A dummy variable indicating if the former policyholder was a smoker.

X₄ = Female = A dummy variable indicating if the former policyholder was female.

a.After adding additional independent variables, what happened to the value of the Rsquare?Does this indicate that the regression model has been improved or made worse?Explain.

b.Using the p-value method, do a hypothesis test for whether there is a statistically significant relationship between a policyholder's gender and his/her age at death.Show all steps to your hypothesis test and use a significance level of 5%.

c.Using the p-value method, do a hypothesis test for whether there is a statistically significant difference between the age at death for policyholders who are smokers vs. nonsmokers.Show all steps to your hypothesis test and use a significance level of 5%.

d.In words, interpret the meaning of the standardized slope coefficient on the Mother variable.

[#4]Concept questions.

(a)What is a linear probability model?In addition, provide an example of how it can be used to study something of interest to a company that sells life insurance. Provide examples of outcomes of interest for which a linear probability model would be appropriate to use.

(b)What is multicollinearity?If you think multicollinearity exists, how can you identify it?

(c)Why is multicollinearity a problem?

(d)Do you think multicollinearity is an issue in the regression results used in Question #3 of this homework (the question that used multivariate regression results on the age at death).

(e)When evaluating the results from a regression analysis, explain how the interpretation of a standardized slope coefficient differs from the interpretation of an unstandardized slope coefficient.

[#5]Application and Extension Proposal

(1)The Homework 1 folder on Canvas includes 4 pdf files with articles from the Harvard Business Review.Read all 4 articles.

(2)Pick 2 articles that interest you the most and then prepare the following:

a.Summarize this article in one paragraph.

b.Explain how regression analysis can be applied to this topic. List a dependent

variable and five independent variables that could be applied to this study.

c.Propose an extension of this research topic and how regression analysis can be

applied in your proposed extension. By "extension," I want you to think of a modification of this topic that future studies could examine.