Include your answers on this test and attach your Megastat output to the test. Clearly mark what it is you are submitting. THE FINAL EXAM DATA is on the course web site, listed as “PA 502 Fall 2013 Exam 3.”

Two-sample hypothesis testing.

Open the Final exam data Excel Workbook and click on the worksheet titled “two-sample” to answer questions below.

The Park Hill School District in the Northland of Kansas City wants to test whether different three different reading programs are more effective than others for accomplishing their educational mission. The three programs will be implemented on an experimental design with random assignment to three groups and post-program comparison (you will do this in the ANOVA problem below).

You are hired to be the statistical consultant and you are tasked to randomly select a group of students and test them for any differences in the pre-test phase the research design. Do a two sample hypothesis tests on whether there is significant differences between the two types of pre-test being considered. IN OTHER WORDS, these are PAIRED OBSERVATIONS!.

1. State the null and alternative hypotheses. Is this a two tail or one tail test?
2. Identify the test statistic. What is the degrees of freedom?
3. What is the critical value(s)?
4. What is the decision rule?
5. Is it reasonable to conclude that is there a difference in the amounts quoted (if so why, if not why not)?

Correlation and Linear Regression:

Use the following to answer questions below. Include your answers on this test and attach your Megastat output to the test. Clearly mark what it is you are submitting.

The data provided are state population based variables, average state income and percentage of state population 25 or older with a college education.

The data are in the Final exam data Excel workbook in the worksheet titled “Correlation and Regression.”

1.What is the statistical association between the two variables? Produce a scatter diagram to support your conclusion.

2.Determine the coefficient of correlation between the two variables. Interpret the value. Do the population hypothesis test of no correlation and state the results.

3.What is the value of the standard error of estimate? Interpret the value in your answer.

1. What is the value of the coefficient of determination?

5.Provide an interpretation of the computed value for the coefficient of determination.

6.What is the regression equation?

Multiple Regression

Please note: this data is ready for analysis in the PA 502 final exam spreadsheet in worksheet “Multiple Regression.”Include your answers on this test and attach your Megastat output to the test. Clearly mark what it is you are submitting.

The state of Missouri has hired you to produce a regression model for predicting average state income. Your first investigation is with an older database of state-level variables. Test the model that the two demographic variables, urbanization, and population density, and two education variables, percent with college degrees and the high school dropout rate.

1. List the dependent variable and the independent variables.
2. Conduct a global test of hypothesis for multiple regression. Use the 0.05 level of significance and state the Critical F value for your decision rule. Explain what the global test of hypothesis means, how do you interpret it in this case?
3. Conduct a test of hypothesis for the individual regression coefficients. Use the 0.05 level of significance. Would you consider deleting any of the independent variables (and explain why, based on the statistics)?

4.What is the value of the standard error of estimate?

5.What is the value of the coefficient of determination? Do you use the adjusted coefficient of determination? If so, what is it?

6.Provide an interpretation of the computed value for the coefficient of determination for all variables, and for each independent variable (use the stepwise selection procedure), and explain which variables you would keep in the model and which you would drop (statistical evidence needs to be included).

Nonparametric Methods

A recent study of the relationship between income and education showed the following results.

 Income Education LT HS HS ASSOC BA/BS Advanced total LT25K 257 653 96 168 66 1240 25-50K 24 203 41 61 31 360 50-75K 4 69 13 54 32 172 GT75K 12 78 23 72 65 250 total 297 1003 173 355 194 2022

1.The appropriate test to analyze the relationship between social activity and education is:

2.The appropriate test statistic for the analysis is a:

3.The null hypothesis for the analysis is:

4.The degrees of freedom for the analysis is:

5.Using 0.05 as the significance level, what is the critical value for the test statistic?

6.What is the value of the test statistic?

1. Which variable is the independent variable, which is the dependent variable, defend your answer?

8.Based on the analysis, what can be concluded?

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