978-0135078228 Chapter 12 Solution Manual Part 2

CASE SOLUTIONS

Case 12.1The Pets, Pets, & Pets Survey

Case Objective: Students must use the proper formulas and interpretations to perform

the various generalization analyses necessary.

Answers to Case Questions

1. How often did Pets, Pets, & Pets customers visit it last year?

x ± zaxs

√

n

=¿

¿4.4 ±1.96 x4.98

√

162

¿4.4 ±1.96 x.39

¿4.4 ±.76

3.6 to 5.2 times

2. How much did they typically spend on the last visit?

x ± zaxs

√

n

=¿

¿18.2±1.96 x8.50

√

162

¿18.2±1.96 x.67

¿18.2±1.31

$16.89 to $19.51

3. How likely are they to buy a Pets, Pets, & Pets on their next visit?

x ± zaxs

√

n

=¿

¿5.3 ±1.96 x1.50

√

162

¿5.3 ±1.96 x.12

¿5.3 ±.23

1

5.1 to 5.5

4. What percent are “regular” Pets, Pets, & Pets customers?

p± zax

√

p x q

n

¿44.4 ±1.96 x

√

44.4 x55.6

162

¿44.4 ±1.96 x3.9

¿44.4 ±7.7

36.7% to 52.1%

5. What percent has recommended Pets, Pets, & Pets to friends?

p± zax

√

p x q

n

¿82.1±1.96 x

√

82.1 x17.9

162

¿82.1±1.96 x3.0

¿82.1±5.9

76.2% to 88.0%

6. The manager at Pets, Pets, & Pets believes that, on average, store customers own

two pets. Is this belief supported by the survey?

z=x−μH

s

√

n

¿1.64−2

.77

√

162

¿−.36

.06

¿−6.0

Because -6.0 is greater than -1.96, the hypothesis is not supported. The confidence

interval is:

x ± zaxs

√

n

=¿

2

¿1.64 ±1.96 x.77

√

162

¿1.64 ±1.96 x.06

¿1.64 ±.12

1.5 to 1.8 pets

7. The manager also believes that Pets, Pets, & Pets monthly newspaper advertising

is highly effective and reaches 80% of the store’s customers. Is this belief

supported by the survey?

z=p−πH

√

pxq

n

¿46.9−80

√

46.9 x53.1

162

¿−33.1

3.9

= –8.49

Because -8.49 is greater than -1.96, the hypothesis is not supported. The

confidence interval is:

p± zax

√

p x q

n

¿46.9 ±1.96 x

√

46.9 x53.1

162

¿46.9 ±1.96 x3.9

¿46.9 ±7.8

39.1% to 54.7%

Case 12.2 Integrated Case: The Advanced Automobile Concepts Survey

Generalization Analysis

Case Objective: Students must use the XL Data Analyst with the Advanced Automobile

Concepts data set to perform and interpret various generalization

analyses.

Answers to Case Questions

3

1. What percent of the American public owns the following type of

vehicle?

The “primary vehicle type” variable is categorical, so compute 95%

confidence intervals to the two answer categories of “economy” and

“standard.”

Primary Vehicle Price Type

Category

Frequenc

y Percent

Lower

Boundar

y

Upper

Boundar

y

2. How does the American public feel about the following statements?

a. Hybrid autos that use alternative fuels will reduce fuel

4

The same metric scale is used for all three statements, so compute

95% confidence intervals for the averages.

Variable Sample Average

Standard

Deviation

Lower

Boundary

Upper

Boundary

Hybrid autos that use

alternative fuels will keep

Hybrid autos that use

alternative fuels will reduce

Hybrid autos that use

alternative fuels will slow

3. Prtincipals at Advanced Automobile Concepts fully understand that

there is resistance to change in Zen.There are some senior

executives who grew up during America’s “romance with the

automobile” era of the 1950s and 1960s and who believe that most

Americans want a large and powerful automobile.These executives

point out that SUVs are extremely popular despite global warming

warnings that have been issued for the past decade and numerous

Hybrid Vehicle Type Probabilit

y

5

Test these hypotheses with the finding from the survey.

Probability is measured with a metric scale, so use the average

Hypothesis Test for an Average

Variable Description Sample

Sample

Average

Hypoth.

Average

Probability of buying a very

small (one-seat) hybrid auto

Does the sample support the hypothesized average?

At 95% level of confidence, this hypothesis is: NOT SUPPORTED

Variable Sample Average

Standard

Deviatio

n

Lower

Boundary

Upper

Boundar

y

Probability of buying a very

small (1 seat) hybrid auto

Hypothesis Test for an Average

Variable Description Sample

Sample

Average

Hypoth.

Average

(two-seat) hybrid auto within 3

6

years

Does the sample support the hypothesized average?

At 95% level of confidence, this hypothesis is: NOT SUPPORTED

Variable

Sampl

e Average

Standard

Deviation

Lower

Boundary

Probability of buying a

small (two-seat) hybrid

Hypothesis Test for an Average

Variable Description Sample

Sample

Average

Hypoth.

Average

Probability of buying an

economy size hybrid auto

Does the sample support the hypothesized average?

At 95% level of confidence, this hypothesis is: NOT SUPPORTED

Variable Sample Average

Standard

Deviation

Lower

Boundary

Upper

Boundary

Probability of buying

an economy size

hybrid auto within 3

7

Hypothesis Test for an Average

Variable Description Sample

Sample

Average

Hypoth.

Average

Probability of buying a standard

Does the sample support the hypothesized average?

At 95% level of confidence, this hypothesis is NOT SUPPORTED

Variable Sample Average

Standard

Deviation

Lower

Boundary

Upper

Boundary

Probability of buying a

standard size hybrid

Hypothesis Test for an Average

Variable Description Sample

Sample

Average

Hypoth.

Average

Probability of buying a large

Does the sample support the hypothesized average?

At 95% level of confidence, this hypothesis is: NOT SUPPORTED

8

Variable Sample Average

Standard

Deviation

Lower

Boundary

Upper

Boundary

Probability of buying

a large size hybrid

3. Using the finding from the survey, estimate the number of

vehicles of each of the following hybrid types that are expected to

be purchased over the next three years.

One must use the 95% confidence intervals for these averages to estimate the population

averages. The lower boundary percent times “There is an estimated 111,617,402

9

Variable Sample Average

Standard

Deviation

Lower

Boundary

Upper

Boundary

Probability of buying a large

The numbers of household estimates are as follows:

10