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 tTest: TwoSample Assuming Unequal Variances.
The next table shows the results of this independent ttest. 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 (ttest, 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 
pvalue (twotailed) 

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 tTest: TwoSample 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 (ttest, 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 
pvalue (twotailed) 

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 pvalue?
Hypothesis Test: Independent Groups (ttest, 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 
pvalue (twotailed) 

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 pvalue? 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 
pvalue 

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 pvalue? 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 
pvalue 

Treatment 
26.13 
2 
13.067 
13.52 
.0008 

Error 
11.60 
12 
0.967 

Total 
37.73 
14 


