Who knows about the t test for a single sample

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Reference no: EM13994368

1. Two boats, the Prada (Italy) and the Oracle (USA), are competing for a spot in the upcoming America's 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 t test 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 t test for a single sample but is unfamiliar with the t test 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

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

 

 

 

Reference no: EM13994368

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