University of Phoenix Material

Week 4 Practice
Worksheet

Prepare a written response to the following questions.

Chapters 9 &11

1. Two boats, the Prada (Italy) and the Oracle (USA), are competing for
a spot in the upcoming Americas Cup race. They race over a part of the course
several times. The sample times in minutes for the Prada were: 12.9, 12.5,
11.0, 13.3, 11.2, 11.4, 11.6, 12.3, 14.2, and 11.3. The sample times in minutes for the Oracle
were: 14.1, 14.1, 14.2, 17.4, 15.8, 16.7, 16.1, 13.3, 13.4, 13.6, 10.8, and
19.0. For data analysis, the appropriate test is the t-Test: Two-Sample
Assuming Unequal Variances.

The next table
shows the results of this independent t-test. At the .05 significance level,
can we conclude that there is a difference in their mean times? Explain these
results to a person who knows about the t
test for a single sample but is unfamiliar with the ttest for independent means.

Hypothesis Test: Independent Groups (t-test,
unequal variance)

Prada

Oracle

12.170

14.875

mean

1.056

2.208

std. dev.

10

12

n

16

df

-2.7050

difference (Prada – Oracle)

0.7196

standard error of difference

0

hypothesized difference

-3.76

t

.0017

p-value
(two-tailed)

-4.2304

confidence interval 95.% lower

-1.1796

confidence interval 95.% upper

1.5254

margin of error

2. The Willow Run Outlet Mall has two Haggar Outlet Stores, one located
on Peach Street and the other on Plum Street. The two stores are laid out
differently, but both store managers claim their layout maximizes the amounts
customers will purchase on impulse. A sample of ten customers at the Peach
Street store revealed they spent the following amounts more than planned:
$17.58, $19.73, $12.61, $17.79, $16.22, $15.82, $15.40, $15.86, $11.82, $15.85.
A sample of fourteen customers at the Plum Street store revealed they spent the
following amounts more than they planned when they entered the store: $18.19,
$20.22, $17.38, $17.96, $23.92, $15.87, $16.47, $15.96, $16.79, $16.74, $21.40,
$20.57, $19.79, $14.83. For Data Analysis, a t-Test: Two-Sample
Assuming Unequal Variances was used.

At the .01
significance level is there a difference in the mean amount purchased on an impulse
at the two stores?Explain
these results to a person who knows about the ttest for a single sample but is unfamiliar with the ttest for independent means.

Hypothesis Test: Independent Groups (t-test,
unequal variance)

Peach
Street

Plum Street

15.8680

18.2921

mean

2.3306

2.5527

std. dev.

10

14

n

20

df

-2.42414

difference (Peach Street – Plum Street)

1.00431

standard error of difference

0

hypothesized difference

-2.41

t

.0255

p-value
(two-tailed)

-5.28173

confidence interval 99.% lower

0.43345

confidence interval 99.% upper

2.85759

margin
of error

3. Fry Brothers heating and Air Conditioning, Inc. employs Larry Clark
and George Murnen to make service calls to repair furnaces and air conditioning
units in homes. Tom Fry, the owner, would like to know whether there is a
difference in the mean number of service calls they make per day. Assume the
population standard deviation for Larry Clark is 1.05 calls per day and 1.23
calls per day for George Murnen. A random sample of 40 days last year showed
that Larry Clark made an average of 4.77 calls per day. For a sample of 50 days
George Murnen made an average of 5.02 calls per day. At the .05 significance
level, is there a difference in the mean number of calls per day between the
two employees? What is the p-value?

Hypothesis Test: Independent Groups (t-test,
pooled variance)

Larry

George

4.77

5.02

mean

1.05

1.23

std. dev.

40

50

n

88

df

-0.25000

difference (Larry – George)

1.33102

pooled variance

1.15370

pooled std. dev.

0.24474

standard error of difference

0

hypothesized difference

-1.02

t

.3098

p-value
(two-tailed)

-0.73636

confidence interval 95.% lower

0.23636

confidence interval 95.% upper

0.48636

margin of error

Chapters 11 & 12

4. A consumer organization wants to know if there is a difference in
the price of a particular toy at three different types of stores. The price of
the toy was checked in a sample of five discount toy stores, five variety
stores, and five department stores. The results are shown below.

Discount toy

Variety

Department

$12

15

19

13

17

17

14

14

16

12

18

20

15

17

19

An ANOVA was run and the results are shown
below. At the .05 significance level, is
there a difference in the mean prices between the three stores? What is the
p-value? Explain why an ANOVA was used
to analyze this problem.

One factor ANOVA

Mean

n

Std. Dev

13.2

5

1.30

Discount Toys

16.2

5

1.64

Variety

18.2

5

1.64

Department

15.9

15

2.56

Total

ANOVA table

Source

SS

df

MS

F

p-value

Treatment

63.33

2

31.667

13.38

.0009

Error

28.40

12

2.367

Total

91.73

14

5. A physician who specializes in weight control has three different
diets she recommends. As an experiment, she randomly selected 15 patients and
then assigned 5 to each diet. After three weeks the following weight losses, in
pounds, were noted. At the .05 significance level, can she conclude that there
is a difference in the mean amount of weight loss among the three diets?

Plan A

Plan B

Plan C

5

6

7

7

7

8

4

7

9

5

5

8

4

6

9

An ANOVA was run and the results are shown
below. At the .01 significance level, is
there a difference in the weight loss between the three plans? What is the
p-value? What can you do to determine
exactly where the difference is?

One factor ANOVA

Mean

n

Std. Dev

5.0

5

1.22

Plan A

6.2

5

0.84

Plan B

8.2

5

0.84

Plan C

6.5

15

1.64

Total

ANOVA table

Source

SS

df

MS

F

p-value

Treatment

26.13

2

13.067

13.52

.0008

Error

11.60

12

0.967

Total

37.73

14

University of Phoenix Material Week 4 Practice
WorksheetPrepare a written response to the following questions.Chapters 9 &111. Two boats, the Prada (Italy) and the Oracle (USA), are competing for
a spot in the upcoming Americas Cup race. They race over a part of the course
several times. The sample times in minutes for the Prada were: 12.9, 12.5,
11.0, 13.3, 11.2, 11.4, 11.6, 12.3, 14.2, and 11.3. The sample times in minutes for the Oracle
were: 14.1, 14.1, 14.2, 17.4, 15.8, 16.7, 16.1, 13.3, 13.4, 13.6, 10.8, and
19.0. For data analysis, the appropriate test is the t-Test: Two-Sample
Assuming Unequal Variances.

The next table
shows the results of this independent t-test. At the .05 significance level,
can we conclude that there is a difference in their mean times? Explain these
results to a person who knows about the t
test for a single sample but is unfamiliar with the ttest for independent means.Hypothesis Test: Independent Groups (t-test,
unequal variance)PradaOracle12.170 14.875 mean1.056 2.208 std. dev.1012n16df-2.7050 difference (Prada – Oracle)0.7196 standard error of difference0hypothesized difference-3.76 t.0017 p-value
(two-tailed)-4.2304 confidence interval 95.% lower-1.1796 confidence interval 95.% upper1.5254 margin of error2. The Willow Run Outlet Mall has two Haggar Outlet Stores, one located
on Peach Street and the other on Plum Street. The two stores are laid out
differently, but both store managers claim their layout maximizes the amounts
customers will purchase on impulse. A sample of ten customers at the Peach
Street store revealed they spent the following amounts more than planned:
$17.58, $19.73, $12.61, $17.79, $16.22, $15.82, $15.40, $15.86, $11.82, $15.85.
A sample of fourteen customers at the Plum Street store revealed they spent the
following amounts more than they planned when they entered the store: $18.19,
$20.22, $17.38, $17.96, $23.92, $15.87, $16.47, $15.96, $16.79, $16.74, $21.40,
$20.57, $19.79, $14.83. For Data Analysis, a t-Test: Two-Sample
Assuming Unequal Variances was used.

At the .01
significance level is there a difference in the mean amount purchased on an impulse
at the two stores?Explain
these results to a person who knows about the ttest for a single sample but is unfamiliar with the ttest for independent means.Hypothesis Test: Independent Groups (t-test,
unequal variance)Peach
StreetPlum Street15.8680 18.2921 mean2.3306 2.5527 std. dev.1014n20df-2.42414 difference (Peach Street – Plum Street)1.00431 standard error of difference0hypothesized difference-2.41 t.0255 p-value
(two-tailed)-5.28173 confidence interval 99.% lower0.43345 confidence interval 99.% upper2.85759 margin
of error3. Fry Brothers heating and Air Conditioning, Inc. employs Larry Clark
and George Murnen to make service calls to repair furnaces and air conditioning
units in homes. Tom Fry, the owner, would like to know whether there is a
difference in the mean number of service calls they make per day. Assume the
population standard deviation for Larry Clark is 1.05 calls per day and 1.23
calls per day for George Murnen. A random sample of 40 days last year showed
that Larry Clark made an average of 4.77 calls per day. For a sample of 50 days
George Murnen made an average of 5.02 calls per day. At the .05 significance
level, is there a difference in the mean number of calls per day between the
two employees? What is the p-value? Hypothesis Test: Independent Groups (t-test,
pooled variance)LarryGeorge4.775.02mean1.051.23std. dev.4050n88 df-0.25000 difference (Larry – George)1.33102 pooled variance1.15370 pooled std. dev.0.24474 standard error of difference0hypothesized difference-1.02 t.3098 p-value
(two-tailed)-0.73636 confidence interval 95.% lower0.23636 confidence interval 95.% upper0.48636 margin of errorChapters 11 & 124. A consumer organization wants to know if there is a difference in
the price of a particular toy at three different types of stores. The price of
the toy was checked in a sample of five discount toy stores, five variety
stores, and five department stores. The results are shown below. Discount toyVarietyDepartment$121519131717141416121820151719An ANOVA was run and the results are shown
below. At the .05 significance level, is
there a difference in the mean prices between the three stores? What is the
p-value? Explain why an ANOVA was used
to analyze this problem.One factor ANOVA MeannStd. Dev 13.2 51.30 Discount Toys16.2 51.64 Variety18.2 51.64 Department 15.9 152.56 Total ANOVA table SourceSS dfMSF
p-valueTreatment63.33 231.667 13.38.0009Error28.40 122.367 Total91.73 14 5. A physician who specializes in weight control has three different
diets she recommends. As an experiment, she randomly selected 15 patients and
then assigned 5 to each diet. After three weeks the following weight losses, in
pounds, were noted. At the .05 significance level, can she conclude that there
is a difference in the mean amount of weight loss among the three diets? Plan APlan BPlan C567778479558469An ANOVA was run and the results are shown
below. At the .01 significance level, is
there a difference in the weight loss between the three plans? What is the
p-value? What can you do to determine
exactly where the difference is?One factor ANOVA MeannStd. Dev 5.0 51.22 Plan A6.2 50.84 Plan B8.2 50.84 Plan C 6.5 151.64 Total ANOVA table SourceSS dfMSF
p-valueTreatment26.13 213.067 13.52.0008Error11.60 120.967 Total37.73 14