Question

The following data give the weight (in kg) of all six employees of a company. 61 73 53 48 68 89

a. Construct the population distribution of the weight of the employees. [3 marks]

b. List all the possible samples of size four (without replacement) that can be selected from this population. [10 marks]

c. Calculate the mean for each of the samples in part (b). [4 marks]

d. Write the sampling distribution of ?̅. [4 marks]

e. Compute the sampling errors for the samples in part (b). [4 marks]

f. Show that ??̅= ? √? √ ?−? ?−1 . [5 marks]

Question 2

a. Find the point estimate of the average systolic pressure of all female in the population. [3 marks]

b. Construct the 95% confidence interval of the average systolic pressure of all female in the population. Briefly explain the confidence interval. [6 marks]

c. Determine the margin of error of estimate for part (b). [2 marks]

d. Find the 98% confidence interval of the average systolic pressure of all female in the population. What conclusion can be drawn from the above confidence interval? [6 marks]

e. State assumption(s) that you make. [2 marks] f. At α = 0.05, can we conclude that the average systolic pressure of all female differs from 128 mmHg? Use p-value approach. [11 marks]

Question 3

a. Write the regression line equation relating the weight and the systolic pressure of the divorced individuals. Interpret the values of the regression coefficients. [8 marks]

b. Identify and interpret the value of the coefficient of correlation. [6 marks]

c. Calculate and elaborate the value of the coefficient of determination. [6 marks]

d. Compute the standard deviation of errors. [5 marks]

e. Estimate the systolic pressure of a divorced individual who weighs 150 pounds. Justify the reliability of the estimate. [4 Marks] f. At the 5% significance level, is there any linear relationship between the weight and the systolic pressure among the divorced individuals? Use the critical value approach. [11 Mark

This list explains the values given for the categories in the data set.

1. “Age” is given in years.

2. “Educational level” values are defined as follows: 0 = no high school 2 = college graduate 1 = high school graduate 3 = graduate degree

3. “Smoking status” values are defined as follows: 0 = does not smoke 1 = smokes less than one pack per day 2 = smokes one or more pack per day

4. “Exercise” values are defined as follows: 0 = none 2 = moderate 1 = light 3 = heavy

5. “Weight” is given in pounds.

6. “Serum cholesterol” is given in milligram percent (mg%).

7. “Systolic pressure” is given in millimeters of mercury (mm Hg).

8. “IQ” is given in standard IQ test score values.

9. “Sodium” is given in milliequivalents per liter per liter (mEq/l).

10. “Gender” is listed as male (M) or female (F).

11. “Marital status” values are defined as follows: M = married S = single W = widowed D = divorced

Answer 1

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