Hypothesis Testing and Confidence Intervals

Project Part B: Hypothesis Testing and Confidence Intervals

 

Your Instructor will provide you with four manager speculations, a.-d., in the Doc Sharing file.

 

Using the sample data, perform the hypothesis test for each of the above situations in order to see if there is evidence to support your manager’s belief in each case a.-d.  In each case use the Seven Elements of a Test of Hypothesis, in Section 6.2 of your text book, using the α provided by your Instructor in the Doc Sharing materials, and explain your conclusion in simple terms.  Also be sure to compute the p-value and interpret.

Follow this up with computing confidence intervals (the required confidence level will be provided by your Instructor) for each of the variables described in a.-d., and again interpreting these intervals.

Write a report to your manager about the results, distilling down the results in a way that would be understandable to someone who does not know statistics.  Clear explanations and interpretations are critical.

 

Submission: The report from part 3 + all of the relevant work done in the hypothesis testing (including Minitab) in 1., and the confidence intervals (Minitab) in 2. as an appendix.

 

Format for report:

 

Summary Report (about 1 paragraph on each of the speculations a.-d.)

Appendix with all of the steps in hypothesis testing (the format of the Seven Elements of a Test of Hypothesis, in Section 6.2 of your text book) for each speculation a.-d. as well as the confidence intervals, the p-values, and including all Minitab output

 

Project Part C: Regression and Correlation Analysis

 

Your Instructor will specify for you the dependent variable and the independent variables in your Case and data.  Using MINITAB perform the regression and correlation analysis for the data by answering the following.

 

Generate a scatterplot for the specified dependent variable and the specified independent variable, including the graph of the “best fit” line. Interpret.

Determine the equation of the “best fit” line, which describes the relationship between the dependent variable and the selected independent variable.

Determine the coefficient of correlation. Interpret.

Determine the coefficient of determination. Interpret.

Test the utility of this regression model (use a two tail test with the α provided by your Instructor). Interpret your results, including the p-value.

Based on your findings in 1-5, what is your opinion about using the designated independent variable to predict the designated dependent variable? Explain.

Compute the confidence interval for beta-1 (the population slope), using the confidence level specified by your Instructor.  Interpret this interval.

Using an interval, estimate the average for the dependent variable for a selected value of the independent variable (to be provided by your Instructor). Interpret this interval.

Using an interval, predict the particular value of the dependent variable for a selected value of the independent variable (to be provided by your Instructor). Interpret this interval.

What can we say about the value of the dependent variable for values of the independent variable that are outside the range of the sample values? Explain your answer.

In an attempt to improve the model, we will attempt to do a multiple regression model predicting the dependent variable based on all of the independent variables.

 

Using MINITAB run the multiple regression analysis using the designated dependent and independent variables.  State the equation for this multiple regression model.

Perform the Global Test for Utility (F-Test). Explain your conclusion.

Perform the t-test on each independent variable. Explain your conclusions and clearly state how you should proceed. In particular, which independent variables should we keep and which should be discarded. If any independent variables are to be discarded, re-run the multiple regression, including only the significant independent variables, and include the final Minitab output, with interpretation.

Is this multiple regression model better than the linear model that we generated in parts 1-10? Explain.

 

Summarize your results from 1-14 in a report that is three pages or less in length and explains and interprets the results in ways that are understandable to someone who does not know statistics.