Economics 201 – Unit 4 Sample Problems

1. If 70% of students own personal computers, what is the probability that from a random sample of 50 students (Hint: use normal approximation to the binomial)

1. exactly 35 will own a personal computer.

2. Assume ACME Fans says that its mean number of defective fans is 22.6 with a standard deviation of 3.8 fans. What is the probability that on a given day:

1. exactly 24 fans will be returned as defective?
2. No less than 20 nor no more than 25 will be returned as defective?
3. No more than 27 fans will be returned as defective?

3. High blood pressure (BP) is a leading cause of strokes. Medical researchers are constantly seeking ways to treat patients suffering from this condition. A specialist claims that aerobic exercise can reduce high BP equally as well as drugs. To test this claim, 25 patients exercised 3 times a week for 60 days and 25 patients took drugs. The percentage reduction in their BP was collected for each group (exercise and drugs). The results are contained in the output below. Based on these data, a) construct a hypothesis test and b) explain your conclusions.

4. Let X = Odometer reading and Y = Trade-in value of a car

n=25 S X_i=913 S Y_i=373 S (X_i – Xbar)² =1341

S (Y_i – Ybar)² =6.84 S (X_i – Xbar) (Y_i – Ybar) = -77.65 S e²_i = 2.34

Based on the above sample data, compute the following:

1. Compute the estimated slope and intercept coefficients
2. Show the sample regression equation
3. Test the significance of the slope estimate at the 5% level of significance.
4. Compute the correlation coefficient and provide an interpretation of its value.
5. Compute the coefficient of determination (R-squared) and provide an interpretation of its value.

5. The president of a company that manufactures car seats has been concerned about the number and cost of welding machine breakdowns. The problem is that machines are old and are becoming unreliable. To determine the need to replace the older machines he collected data on age of the welding machines and the cost of the repairs. He computed regression results shown below. Your job is to do the following:

a) show the sample regression line (equation) ; b) interpret each of the coefficients; c) provide an explanation of the coefficient of determination [R square]. d) test the significance of the estimated slope parameter (at the 5% level)