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 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
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
Jermaine Byrant
Nicole Johnson
OVER
RATING
YEARS
