1. In a study to evaluate the effect of a new blood pressure medication on systolic blood pressure, 12 patients were given the drug. Their blood pressure was measured before the new drug and following an appropriate time interval. A paired t test was used to determine whether the drug was effective in lowering blood pressure and the following analysis was obtained:

1. State the research hypothesis in plain English.
2. State the null hypothesis in plain English.
3. Should this problem be done using a 2 tailed test or 1 tailed test and why?
4. What is the average effect of the drug on blood pressure (state direction)?
5. What is the correct p value and why?

f. Should the null hypothesis be retained or rejected at the .05 level and why?

g. Should the null hypothesis be retained or rejected at the .01 level and why?

2 . For this problem, we want to find out whether Heart Rate varies by BMI category. First, use Data/Select Cases to eliminate those few underweight individuals in the sample. Use a one-way ANOVA, specifying descriptive statistics under Options, to get descriptive data and the ANOVA table, and requesting a post hoc comparison using the Tukey procedure.

1. What research question can be answered by the 1 way ANOVA?
2. Suggest a rationale that would support this research hypothesis.
3. What would the null hypothesis be?
4. Why is this problem done as ANOVA instead of a t test?
5. How is the F calculated from other values in the ANOVA table (show figures)?
6. Should the null hypothesis be retained or rejected at the .05 level and why? State your conclusion in statistical terms and plain English.
7. Should the null hypothesis be retained or rejected at the .01 level and why? State your conclusion in statistical terms and plain English.

h. Was the post hoc test appropriate in this case, and do the results provide any additional information not indicated by the 1 way ANOVA? Explain.

i. .Explain why this analysis might be better done using the original BMI variable instead of the recoded one. In that case, what type of analysis would you do and what would you expect to find.

3. For this problem, using the sampleFHS data base, we want to use 2 way ANOVA to find out whether Heart Rate varies by BMI category or gender, as well as whether there is any interaction. First, use Data/Select Cases to eliminate those few underweight individuals in the sample. Then go to the General Linear Model to request the analysis, adding the dependent variable and fixed factors, and requesting descriptive statistics under options. Click Plots and enter BMI categories as the horizontal axis and sex as separate lines, click Add to request the plot, click Continue, and then click OK.

1. What 3 research hypotheses can be tested by this analysis (state clearly in plain English, ie don’t say "interaction")?
2. What are the 3 corresponding null hypotheses? (State clearly in plain English, ie don’t say "no interaction")
3. Using alpha=.01, explain the results for BMI and heart rate, in both statistical terms and plain English.
4. Using alpha=.01, explain the results for sex and heart rate, in both statistical terms and plain English.
5. Using alpha=.01, explain the results for interaction, in both statistical terms and plain English.

4 . For this problem, we will construct a regression model to predict serum cholesterol from systolic bp and smoking (yes/no) . First, use Data Select Cases to Select All Cases. Use Analyze/Regression/Linear to do a regression analysis for predicting serum cholesterol from systolic bp and smoking by entering the appropriate dependent and independent variables. Select Stepwise as the method of analysis. Use Statistics to select regression coefficient estimates and model fit , then click Continue and OK.

QUESTIONS a-g REFER TO MODEL 1 OF THIS ANALYSIS:

a. State the research hypothesis in plain English.

b. State the null hypothesis in plain English.

b. Explain why N=1366 when there are 1459 people in the data base.

d . Should the null hypothesis be retained or rejected, using alpha = .01, and how do you know?

e. State the results in plain English.

f. What is the prediction equation according to this analysis (be specific, ie don’t use x and y in the equation)? Explain in plain English exactly what this equation tells you.

g. What would be the predicted serum cholesterol for a person with systolic bp of 110? 120? 130? SHOW ALL CALCULATIONS.

QUESTIONS h- p REFER TO MODEL 2 OF THIS ANALYSIS:

h. Which of the independent variables is the best predictor of serum cholesterol and how do you know?

i. How do you account for the difference in % of variance explained by model 2 vs. model 1?

j. Did the addition of the second predictor result in a significant increase (alpha=.05) in % of variance explained? Explain your answer.

k. What is the prediction equation according to this analysis (be specific, ie don’t use x and y in the equation)? Explain in plain English exactly what this equation tells you.

l. Explain why the regression coefficient for systolic BP is not the same for Models 1 and 2.

m. What would be the predicted serum cholesterol for a person with systolic bp of 110 , 120, and 130 , for nonsmokers? SHOW ALL CALCULATIONS.

n. What would be the predicted serum cholesterol for a person with systolic bp of 110 , 120, and 130 , for smokers? SHOW ALL CALCULATIONS.

o. Describe the effect of smoking on serum cholesterol, controlling for systolic bp.

p. Describe the effect of systolic bp on serum cholesterol, controlling for smoking.

5-For the effect of gender on heart rate (referring back to problem 3 data),

1. use the F table in the text to determine what critical F would be required to reject the null hypothesis at the:
   .10 level?
   .05 level?
   .01 level?
2. use the probability calculator to determine what critical F would be required to reject this null hypothesis at the:

1. .10 level?
2. .05 level?
3. .01 level?

c. Explain why these values are not exactly the same.

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Deliverable: Word Document