c. How many observations are in the data set?

4. Which of the variables are qualitative and which are quantitative variables?

2. Help two admissions counselors at a large university settle a debate about the qualifications of men and women admitted into the M.B.A. program. You are given the following data from a sample of 400 business students. Remember that your role is to clearly summarize and communicate some simple results. Be as thorough as possible.

• There are 240 females in the sample.
• Of the females, 24 had scores of less than 20 on the ACT, 168 scored between 20-25, and 48 scored higher than 25.
• Of the males, 40 had scores of less than 20 on the ACT, 96 scored between 20-25, and 24 scored higher than 25.

a. Create a cross-tabulation that summarizes the above information. Label your rows, columns and totals of both rows and columns. (8 points)

b. Use relative frequencies, in two separate cross-tabs, to analyze both the rows and columns of data. What can you tell the counselors about gender differences in test scores of their business students? (12 points)

3. The number of hours worked per week for a sample of 10 students is shown below.

a. Compute two measures of dispersion and explain their meanings. (5 points)

b. Determine the mean and median and explain their meanings and relationship to one another. (4 points)

c. Compute the 70^th percentile and explain its meaning. (4 points)

 4. The average wage of Tennessee cashiers is $14 with a standard deviation of $4.20. In Georgia, the average wage of cashiers is $16 with a standard deviation of $4.40. In which state do the wages of cashiers appear to be more dispersed? Explain. (5 points)

5. Suppose that a high school senior has applied to Hanover College and is eligible for a Merit scholarship (M) and an Athletic scholarship (A). The probability that she receives an athletic scholarship is .18. The probability she receives both scholarships is .11. The probability of getting at least one of the scholarships is .3. (Hint: drawing a probability tree might help.)

a. What is the probability that she will receive a Merit scholarship? (2 points)

b. Are events A and M mutually exclusive? Why or why not? Explain using intuition and probabilities. (8 points)

c. Are events A and M independent events? Why or why not? Explain using intuition and probabilities. (8 points)

d. How could a high school guidance counselor use this information to assist this student in planning to pay for her college education? (8 points)

6. A salesperson contacts 8 potential customers per day. From past experience, we know that the probability of a potential customer making a purchase is .10.

a. If this person needs at least 3 sales to pay his cell phone bill, what’s the probability he is able to do so? (5 points)

b. Every time our salesperson has a day without any sales, he is forced to watch motivational tapes in his boss’ office and listen to his boss rant about the good old days when workers cared about their jobs. In the next 4 weeks (20 workdays), how many days can he expect to watch the videos and listen to the harassment? (6 points)

7. A security guard at the Hamilton Place Mall needs 5 extra minutes of lunch so he can sneak a day old roll at Cinnabon. As his boss, you are concerned that in those 5 unattended minutes, a shoplifting incident might occur at the Baby Gap store. If the guard isn’t present at the time of the shoplifting, you’ll be forced to fire him. From experience, you know that shoplifting at Baby Gap occurs at a rate of 1 per 30 minutes. What’s the probability you fire the guard’s sorry butt? How would his job be more secure if security cameras are installed that reduce the number of shoplifting incidents to a rate of 2 per 90 minutes? (9 points)

8. Hanover College Student Programming Board (SPB) is going to create a dating game for next Saturday night and you’ve been hired to do some statistical consulting. A survey of students indicates that exactly 40% of men at Hanover are in a serious dating relationship. SPB plans to bring 50 male students to a lecture hall as a pool of potential bachelors for the dating game. SPB plans to select 5 male students at random, and they need exactly 3 male students that are not involved in a serious dating relationship. As a consultant, what would be your analysis? Any suggestions for the planners? (8 points)