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

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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.

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.
4. 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.”

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

Please note: this data is ready for analysis in the PA 502 exam 3 spreadsheet in worksheet “Nonparametric.”Include your answers in this file, and cut and paste your Megastat output beneath your answer if applicable.

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?
7. Which variable is the independent variable, which is the dependent variable, defend your answer?
8. Based on the analysis, what can be concluded?

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