Provide a response to the following questions.
Note: Each team member should compute the following questions and submit to the Learning Team forum. The team should then discuss each team member's answers to ascertain the correct answer for each question. Once your team has answered all the questions, submit a finalized team worksheet.
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 as follows: 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 as follows: 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 you 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 who is unfamiliar with the t test for independent means.
Hypothesis Test: Independent Groups (t test, unequal variance)
|
Prada
|
Oracle
|
|
|
|
|
|
| |
12.170
|
14.875
|
mean
|
|
|
|
|
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1.056
|
2.208
|
std. dev.
|
|
|
|
|
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10
|
12
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n
|
|
|
|
|
| |
|
|
|
|
|
|
|
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|
16
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df
|
|
|
|
|
| |
|
-2.7050
|
difference (Prada - Oracle)
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|
|
| |
|
0.7196
|
standard error of difference
|
|
|
| |
|
0
|
hypothesized difference
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|
|
| |
|
|
|
|
|
|
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-3.76
|
t
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|
|
|
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| |
|
.0017
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p-value (two-tailed)
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|
|
|
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|
|
|
|
|
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-4.2304
|
confidence interval 95.% lower
|
|
|
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-1.1796
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confidence interval 95.% upper
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|
|
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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 10 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 14 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 who 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
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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
|
|
|
|