PRACTICE (Midterm)

1. Monthly rent data in dollars for a sample of 10 one-bedroom apartments in a small town in Iowa are given below:

220 216 220 205 210 240 195 235 204 250

a. Compute the sample monthly average rent

b. Compute the sample median

c. What is the mode?

d. Describe briefly what each statistic in parts a. to c. tells you about the data.

2. Suppose that a firm’s sales were $2,500,000 four years ago, and sales have grown annually by 25%, 15%, -5%, and 10% since that time. What was the geometric mean growth rate in sales over the past four years?

3. Suppose that a firm’s sales were $3,750,000 five years ago and are $5,250,000 today. What was the geometric mean growth rate in sales over the past five years?

4. A basketball player has the following points for seven games: 20, 25, 32, 18, 19, 22, and 30. Compute the following measures of central location and variability: a. mean

b. median

c. standard deviation

d. coefficient of variation

5. The annual percentage rates of return over the past 10 years for two mutual funds are as follows:

Fund A: 7.1 -7.4 19.7 -3.9 32.4 41.7 23.2 4.0 1.9 29.3

Fund B: 10.8 -4.1 5.1 10.9 26.5 24.0 16.9 9.4 -2.6 10.1

Which fund would you classify as having the higher level of risk?

6. A supermarket has determined that daily demand for egg cartons has an approximate mound-shaped distribution, with a mean of 55 cartons and a standard deviation of six cartons. a. For what percentage of days can we expect the number of cartons of eggs sold to be between 49 and 61? b. For what percentage of days can we expect the number of cartons of eggs sold to be more than 2 standard deviations from the mean? c. If the supermarket begins each morning with a stock of 77 cartons of eggs, for what percentage of days will there be an insufficient number of cartons to meet the demand?

7. A sample of 12 measurements has a mean of 25 and a standard deviation of 4. Suppose that the sample is enlarged to 14 measurements, by including two additional measurements having common value of 25 each. a. Find the mean of the sample of 14 measurements.

b. Find the standard deviation of the sample of 14 measurements.

8. Given the following sample data

x| 420| 610| 625| 500| 400| 450| 550| 650| 480| 565| y| 2.80| 3.60| 3.75| 3.00| 2.50| 2.70| 3.50| 3.90| 2.95| 3.30|

a. Calculate the covariance and the correlation coefficient. b. Comment on the relationship between x and y.

c. Draw the scatter diagram and plot the least squares line.

9. A Ph.D. graduate has applied for a job with two universities: A and B. The graduate feels that she has a 60% chance of receiving an offer from university A and a 50% chance of receiving an offer from university B. If she receives an offer from university B, she believes that she has an 80% chance of receiving an offer from university A. a. What is the probability that both universities will make her an offer? b. What is the probability that at least one university will make her an offer? c. If she receives an offer from university B, what is the probability that she will not receive an offer from university A?

10. There are three approaches to determining the probability that an outcome will occur: classical, relative frequency, and subjective. Which is most appropriate in determining the probability of the following outcomes? a. The unemployment rate will rise next month.

b. Five tosses of a coin will result in exactly two heads. c. An American will win the French Open Tennis Tournament in the year 2000. d. A randomly selected woman will suffer a breast cancer during the coming year.

11. At the beginning of each year, an investment...