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# Regression, plots and coeffcicent of variation

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37. A regional commuter airline selected a random sample of 25 flights and found that the
correlation between the number of passengers and the total weight, in pounds, of luggage
stored in the luggage compartment is 0.94. Using the .05 significance level, can we
conclude that there is a positive association between the two variables?

40. A suburban hotel derives its gross income from its hotel and restaurant operations. The
owners are interested in the relationship between the number of rooms occupied on a
nightly basis and the revenue per day in the restaurant. Below is a sample of 25 days
(Monday through Thursday) from last year showing the restaurant income and number of
rooms occupied. Use a statistical software package to answer the following questions.

a. Does the breakfast revenue seem to increase as the number of occupied rooms
increases? Draw a scatter diagram to support your conclusion.
b. Determine the coefficient of correlation between the two variables. Interpret the value.
c. Is it reasonable to conclude that there is a positive relationship between revenue and
occupied rooms? Use the .10 significance level.
d. What percent of the variation in revenue in the restaurant is accounted for by the number
of rooms occupied?

Day Income Occupied Day Income Occupied
1 \$1,452 23 14 \$1,425 27
2 1,361 47 15 1,445 34
3 1,426 21 16 1,439 15
4 1,470 39 17 1,348 19
5 1,456 37 18 1,450 38
6 1,430 29 19 1,431 44
7 1,354 23 20 1,446 47
8 1,442 44 21 1,485 43
9 1,394 45 22 1,405 38
10 1,459 16 23 1,461 51
11 1,399 30 24 1,490 61
12 1,458 42 25 1,426 39
13 1,537 54

42. Martin Motors has in stock three cars of the same make and model. The president would
like to compare the gas consumption of the three cars (labeled car A, car B, and car C)
using four different types of gasoline. For each trial, a gallon of gasoline was added to
an empty tank, and the car was driven until it ran out of gas. The following table shows
the number of miles driven in each trial.
Using the .05 level of significance:

a. Is there a difference among types of gasoline?
b. Is there a difference in the cars?

Distance (miles)
Types of Gasoline Car A Car B Car C
Regular 22.4 20.8 21.5
Super regular 17.0 19.4 20.7

58. The amount of income spent on housing is an important component of the cost of living.
The total costs of housing for homeowners might include mortgage payments, property
taxes, and utility costs (water, heat, electricity). An economist selected a sample of
20 homeowners in New England and then calculated these total housing costs as a percent
of monthly income, five years ago and now. The information is reported below. Is it
reasonable to conclude the percent is less now than five years ago?

Homeowner Five Years Ago Now Homeowner Five Years Ago Now
1 17% 10% 11 35% 32%
2 20 39 12 16 32
3 29 37 13 23 21
4 43 27 14 33 12
5 36 12 15 44 40
6 43 41 16 44 42
7 45 24 17 28 22
8 19 26 18 29 19
9 49 28 19 39 35
10 49 26 20 22 12

Chapter 10 -42. During recent seasons, Major League Baseball has been criticized for the length of the
games. A report indicated that the average game lasts 3 hours and 30 minutes. A sample
of 17 games revealed the following times to completion. (Note that the minutes have
been changed to fractions of hours, so that a game that lasted 2 hours and 24 minutes
is reported at 2.40 hours.)

Can we conclude that the mean time for a game is less than 3.50 hours? Use the .05
significance level.

2.98 2.40 2.70 2.25 3.23 3.17 2.93 3.18 2.80
2.38 3.75 3.20 3.27 2.52 2.58 4.45 2.45

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#### Solution Summary

37. A regional commuter airline selected a random sample of 25 flights and found that the
correlation between the number of passengers and the total weight, in pounds, of luggage
stored in the luggage compartment is 0.94. Using the .05 significance level, can we
conclude that there is a positive association between the two variables?

40. A suburban hotel derives its gross income from its hotel and restaurant operations. The
owners are interested in the relationship between the number of rooms occupied on a
nightly basis and the revenue per day in the restaurant. Below is a sample of 25 days
(Monday through Thursday) from last year showing the restaurant income and number of
rooms occupied. Use a statistical software package to answer the following questions.

\$2.19