**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, S_{x}, and S_{y}.

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.