Broward Community College

Math Dept.

Statistics STA2023

Test # 5

 

1-) Each box of Healthy Crunch breakfast cereal contains a coupon entitling you to a free package of  garden seeds. At the Healthy Crunch home office they use the weight of incoming mail to    determine how many of their employees are to be assigned to collecting coupons and mailing out     seed packages on a given day. (Healthy Crunch has a policy of answering all its mail the day it is     received.)

                Let x be the weight of incoming mail and y be the number of employees required to process the mail in one working day. A random sample of 8 days gave the following data.

 

X(lb)

11

20

16

6

12

18

23

25

Y(No.of employees)

6

10

9

5

8

14

13

16

 

                a-) Draw a scatter plot for the data

                b-) Find x, y, Sx, and Sy.

                c-) Find a and b and write the equation of the least-squares (regression) line.

                d-) Graph the least-squares (regression) line on your scatter plot

                e-) If Healthy Crunch receives 15 lb of mail, how many employees should be assigned mail duty?     

                 f-) Find, r. What proportion of the variation of the number of employees can be explained by the linear relationship between the weight of incoming mail and the number of employees?  

                g-) Construct a residual plot.

                    h-) What does the residual plot suggest about the relationship between number of employees and the weight of incoming mail?

 

2-)  The distribution of types of households for the U.S. population and a random sample of 411   households in the community of Dove Creek, Montana are shown below (based on Statistical          Abstract of the United States).

 

Type of Household

% of U.S. Household

Observed # in Dove Creek

Married, with children

26%

102

Married, no children

29%

112

Single parent

9%

33

One person

25%

96

Other(e.g., roommates, siblings)

11%

68

               

                Use a 5% level of significance to test the claim that the distribution of U.S. households fits the    Dove Creek distribution.

 

3-) Mr. Acosta, a sociologist, is doing a study to see if there is a relationship between the age of a   young adult (18 to 35 years old) and the type of movie preferred. A random sample of 93 adults     revealed the following data. Test if age and type of movie preferred are independent at the 0.05 level.

 

Movie

18-23 yr

24-29 yr

30-35 yr

Musical

8

15

11

Science Fiction

12

10

8

Comedy

9

8

12

 

 

4-)   Mars, Inc. claims that its M&M candies are distributed with the color percentages given in the tables. Use your bag of candies to test the claim that the color distributed is as claimed by Mars,      Inc. Use a 0.05 significance level.

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