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.
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
The previous 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.
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.
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
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.
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.
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
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?
An organizational psychologist measures levels of job satisfaction in a sample of 30 participants. To measure the variance of job satisfaction, it is calculated that the SS = 120 for this sample.
What are the degrees of freedom for the variance?
Compute the variance and standard deviation (you will have to do this one by hand).
