# Descriptive statistics and correlation

12. A specialty bookstore concentrates mainly on used books. Paperbacks are $1.00 each, and hardcover books are $3.50. Of the 50 books sold last Tuesday morning, 40 were paperback and the rest were hardcover. What was the weighted mean price of a book?

59. A major cost factor in the purchase of a home is the monthly loan payment. There are many Websites where prospective home buyers can shop the interest rates and determine their monthly payment. Capital Bank of Virginia is considering offering home loans on the Web. Before making a final decision, a sample of recent loans is selected and the monthly payment noted. The information is organized into the following frequency distribution.

Monthly Mortgage Payment Number of Homeowners

$ 100 up to $ 500 1

500 up to 900 9

900 up to 1,300 11

1,300 up to 1,700 23

1,700 up to 2,100 11

2,100 up to 2,500 4

2,500 up to 2,900 1

Total 60

a. Determine the mean monthly payment.

b. Determine the median monthly payment.

106. Listed below are the salaries for the New York Yankees for the year 2000. The salary information

is reported in millions of dollars.

$9.86 $9.50 $8.25 $6.25 $6.00 $5.95

5.25 5.00 4.33 4.30 4.25 3.40

3.13 2.02 2.00 1.90 1.85 1.82

0.80 0.38 0.35 0.35 0.20 0.20

0.20 0.20 0.20 0.20 0.20

a. Determine the mean, median, and the standard deviation.

b. Determine the coefficient of skewness using Pearsonâ??s method.

c. Determine the coefficient of skewness using the software method.

297. A new sports car model has defective brakes 15 percent of the time and a defective steering mechanism 5 percent of the time. Let's assume (and hope) that these problems occur independently. If one or the other of these problems is present, the car is called a 'lemon'. If both of these problems are present, the car is a 'hazard'. Your instructor purchased one of these cars yesterday. What is the probability it is:

a. A lemon?

b. A hazard?

292. Reynolds Construction Company has agreed not to erect all ook-alike' homes in a new subdivision.

Five exterior designs are offered to potential home buyers. The builder has standardized three

interior plans that can be incorporated in any of the five exteriors. How many different ways can

the exterior and interior plans be offered to potential home buyers?

295. A new chewing gum has been developed that is helpful to those who want to stop smoking. If 60 percent of those people chewing the gum are successful in stopping smoking, what is the probability that in a group of four smokers using the gum at least one quits smoking?

299. There are four people being considered for the position of chief executive officer of Dalton Enterprises.

Three of the applicants are over 60 years of age. Two are female, of which only one is over 60.

a. What is the probability that a candidate is over 60 and female?

b. Given that the candidate is male, what is the probability he is less than 60?

c. Given that the person is over 60, what is the probability the person is female?

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#### Solution Summary

. A specialty bookstore concentrates mainly on used books. Paperbacks are $1.00 each, and hardcover books are $3.50. Of the 50 books sold last Tuesday morning, 40 were paperback and the rest were hardcover. What was the weighted mean price of a book?

Determine the mean, median, and the standard deviation.

Determine the coefficient of skewness using Pearson's method.

Determine the coefficient of skewness using the software method.

Descriptive Statistics, Correlation, T-Test, ANOVA

This exercise requires you to use an electronic spreadsheet, such as Microsoft's Excel, to compute information about a data set. The data set is shown in Table 1 below. There are three groups in the complete data set:

Group 1 Learning via the Lecture method of instruction

Group 2 Learning via the Cooperative method of instruction

Group 3 Learning via Computer-based instruction

The scores in each group are the final examination scores of students in the three groups. The scores represent overall knowledge learned under each method of instruction. The higher the score, the more knowledge learned. The Independent and Dependent variables are:

Independent variable - the method of instruction at three levels: Lecture, Cooperative, and Computer.

Dependent variable - the final examination score.

A B C

1 Group 1 Group 2 Group 3

2 78 45 77

3 88 54 75

4 96 65 34

5 77 47 88

6 83 77 97

7 85 61 69

8 90 53 45

9 85 69 90

10 95 70 85

11 68 45 66

a. Compute the descriptive statistics for Group 1.

As a check on your work for Group 1 you should obtain the following:

Mean 84.5

Standard Error 2.704933764

Meadian 85

Mode 85

Standard deviation 8.553751614

Sample Variance 73.16666667

Kurtosis 0.13658086

Skewness -0.51130504

Range 28

Sum 845

Count 10

Largest 96

Smallest 68

Confidence level (95.0%) 6.118989952

b. Calculate the correlation coefficient between Groups 1 and 2.

c. Perform a t-Test between Groups 1 and 2.

d. Perform analysis of variance (ANOVA)

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