1. The heart rates of 15 men between the ages of 70 and 95 were measured before and after participating in a three-month exercise program.

Subject Before After After-Before Difference, d

1 88 90 2

2 94 91 -3

3 99 99 0

4 101 98 -3

5 96 97 1

6 91 91 0

7 88 90 2

8 101 95 -6

9 105 100 -5

10 98 100 2

11 96 94 -2

12 98 97 -1

13 87 84 -3

14 88 82 -6

15 91 90 -1

1. 
   Calculate the paired t-test and Wilcoxon Signed Ranks test with a 0.10 significance criterion?
2. 
   Briefly interpret the results of the t-test. What conclusions can you make about the effect of the exercise program on the heart rates of these elderly men?

3. The data below represent four different treatments (diets) that were fed to a sample of 28 healthy adults for 12 weeks. The dependent measure is weight loss (lbs). The research question is: Does diet impact weight loss in healthy adults?

Food Pyramid

(Control) Group Atkins Diet NutriSystem South Beach

6.6 10.1 12.3 8.1

4.7 5.0 10.4 9.9

8.7 7.8 4.5 7.0

2.9 4.8 8.9 10.9

1.1 12.7 7.2 11.8

3.3 3.0 14.5 6.2

5.4 4.5 8.4 6.6

1. 
   Calculate and report the appropriate statistical test(s) for these data.
2. 
   Provide a brief conclusion about the results of your analysis. [Hint: Answer the question of interest.]

4. A research report states that: "A comparison of the 90 normal patients to the 10 patients with hypotension shows that only 6.7% of the former group died as compared to 40% of the latter."

1. Put the data into a 2 X 2 contingency table and test the significance of blood pressure as a prognostic sign using a Chi-square test.
2. 
   Provide a brief conclusion about the results of your analysis

5. Water quality in Philadelphia has been recently analyzed. Trace metals in drinking water affect the flavor of the water, and unusually high concentrations can pose a health hazard. The following table shows trace-metal concentrations (zinc, in mg/liter) for both surface water and bottom water at 10 different Schuylkill river locations. The aim is to see if surface water concentration (x) is predictive of bottom water concentration (y).

Zinc concentration (mg/liter)

Location Bottom Surface

1 0.430 0.415

2 0.266 0.238

3 0.567 0.390

4 0.531 0.410

5 0.707 0.605

6 0.716 0.609

7 0.354 0.321

8 0.497 0.467

9 0.631 0.619

10 0.399 0.314

1. Plot a scatterplot to show a possible association between the concentrations. Check to see if a linear model is justified.
2. 
   Estimate the regression parameters, estimate the bottom water concentration for location with a surface water concentration of 0.5 mg/L, and draw the regression line on the same graph with the scatterplot.
3. 
   Based on the data provided in question #5,

1. Test to see if the two concentrations are independent, state your hypotheses and your choice of the test size.
2. Calculate the coefficient of determination and provide a brief interpretation.

6. You conduct an experiment and calculate that the two-tailed p-value is (p = 0.09).

1. What is the one-tailed p-value?
2. Identify and briefly explain two assumptions that you made.

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