Solution-Explain a possible relationship between variables

1. An insurance representative wants to determine if the proportions of women and men who buy the different policy types are the same. The actual sales results for 50 women and 50 men are

Policy A Policy B

Women 18 32

Men 12 38

Under the null hypothesis, what is the expected number of men who would buy Policy B?

A)  50    B)  25    C)  30    D)  35

2. A chewing gum manufacturer wishes to determine if his customers prefer one flavor gum to any other flavor. He selects a random sample of customers and records the flavor of gum that is purchased.  Determine the test value for the data given.

Type Number Sold

Spearmint 25

Wintergreen 32

Cherry 18

Cinnamon 43 

A)  11.56     B)  6.18     C)  18.0     D)  29.5 

3. A health club has six tennis courts.  The owner hypothesizes that his patrons have no preference for a particular court.  He observes how many people play on each court on a particular day.  Compute the expected value for the data shown below.

Court Number of Players

1 9

2 10

3 11

4 6

5 14

6 7

A)  4.37     B)  10.3     C)  9.5     D)  5.72 

4. A software company wants to determine whether there is a relationship between their three sales offices and the sales of their software products. The actual sales results are

Product A Product B Product C

Office 1 18 8 24

Office 2 15 22 13

Office 3 21 16 63

Under the null hypothesis, what is the expected number of Product A that would be sold by Office 2?

A)  27.00    B)  10.80    C)  13.50    D)  18.00

5. A contingency table is made up of 8 rows and 4 columns.  How many degrees of freedom are present? 

A)  24     B)  21     C)  28     D)  32 

Use the following to answer questions 15-16:

A four-year university has decided to implement a new approach to teaching Statistics.  Full-time and adjunct professors were surveyed to determine whether they preferred the traditional lecture approach or a computer approach to teaching Statistics.  Use hypothesis testing to test the independence of opinion between the two groups.

Table 11-3 

PreferLecture PreferComputer NoPreference

Full-time 8 13 6

Adjunct 11 22 10

6. Calculate the expected value of an adjunct professor who prefers to lecture. 

A)  21.50     B)  9.83     C)  11.67     D)  7.33

7. What is the expected value of an adjunct professor who prefers computer instruction? 

A)  11.67     B)  21.50     C)  9.83     D)  13.50 

8 Which of the following assumptions is not made for the F test for comparing three or more means?

A) The populations from which the samples were obtained must be normally distributed

B) The samples must be independent of each other

C) The sample sizes must be equal.

D) The variances of the populations must be equal

9. Compute the intercept of the regression line for the data below.

X values –5 1 4

Y values 7 6 –2

A)  3.46    B)  3.67    C)  7.06    D)  –1.55

10. Compute the intercept of the regression line for the data below.

X values –3 1 5 8

Y values 3 2 –3 0

A)  2.22    B)  1.60    C)  2.93    D)  1.77

11. In a regression model y’ = –10 + 2x, if the value of x changes by -3, then the actual value of y will have

A)  decrease by 30    B)  increase by 3    C)  decrease by 6    D)  cannot be determined

12. A study was conducted to determine if there was a relationship between the prices a non-member of a club paid for various publications and the prices that a member paid for the same publications.    The data gathered is shown below.

Non-member Member

Price x,   Price y,

58 32

42 22

46 20

32 16

25 19

75 58

35 34

63 48 

What is the value of the correlation coefficient?

A)  0.857     B)  0.679     C)  0.932     D)  0.762 

13. In a regression model y’ = –8 – 5x, if the x value increases by 2, then the predicted value for y will change by

A)  –10     B)  –8    C)  8    D)  10

14. A researcher has reason to be that, for an experiment with 50 points, a 95% prediction interval would be of width 4. If the researcher wishes to run a more precise experiment that will result in a 95% prediction interval of width 2, then the researcher will require

A)  200 points    B)  More than 200 points    C)  50 points     D)  25 points

15. Which of the following does not explain a possible relationship between variables when the null hypothesis is rejected? 

A) negative effect C) direct cause-and-effect 

B) caused by a third variable D) reverse cause-and-effect 

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