Two sample Means Tests
Name___________________________
1. College financial aid offices expect students to use summer earnings to help pay for college. But how large
are these earnings? They studied 1296 students. The mean for 675 males was $1884.52 37 while the mean
for the 621 female students was $1360.39. The standard deviation for the males is known to be $1884.52
and the standard deviation for the females is known to be $1037.46. Does the data provide evidence that
the mean earnings from male students is greater than that of the females?
2. American League baseball teams play their games with the designated hitter rule, meaning that the pitchers
do not bat. The league believes that replacing the pitcher, traditionally a weak hitter, with another player in
the batting order produces more runs and generates more interest among fans. Below are the average
numbers of runs scored in the American League and the National League stadiums for the first half of the
2001 season. Does the data provide evidence that the American League scored more runs on average than
the National League?
American
11.1
10.3
9.4
10.8
10.1
9.3
9
10.8
10
9.2
8.3
10.3
9.5
9.2
National
14
10.2
9.5
8.3
11.6
9.5
9.1
8.2
10.4
9.5
8.8
8.1
10.3
9.5
8.4
7.9
3. This test was administered to a group of 40 students in the morning and they averaged a score of 900 with a
standard deviation of 50 points. It was then administered to 42 students in the afternoon who scored an
average of 920 with a standard deviation of 30 points. Researchers are testing the claim that students will
perform better on a standardized test in the afternoon. Use a 5% level of significance.
4. Some archaeologists theorize that ancient Egyptians interbred with several different immigrant populations
over thousands of years. To see if there is any indication of changes in body structure that might have
resulted, they measured 30 skulls of male Egyptians dated from 4000 B.C.E. and 30 others dated from 200
B.C.E. Do these data provide evidence that the mean breadth of males’ skulls changed over this time period?
4000 B.C.E.
131
134
135
125
126
134
131
132
128
119
141
130
136
131
138
138
135
128
125
132
127
131
139
131
134
132
124
129
126
131
2000 B.C.E.
141
134
144
141
135
141
135
133
130
133
136
133
131
134
138
140
131
131
139
129
136
140
136
132
138
131
135
132
139
141
5. The fire department tested two types of fire extinguishers on gasoline fires. It set 10 gallons of gasoline
ablaze and then timed how long it took to extinguish the blaze using one extinguisher. This process was
repeated six times using a random sample of type I extinguishers. The mean time to put out the blazes was
12.2 minutes with a standard deviation of 2.8 minutes. Six more blazes of the same type were started and
type II extinguishers were used. The mean time for this sample was 15 minutes with a standard deviation of
2.8 minutes. Use a 5% level of significance to test the claim that it takes longer on average to put out the
gasoline fire using a type II extinguisher.
6. Maureen is a cocktail hostess in a very exclusive private club. The IRS is auditing her tax return this year.
Maureen claims that her average tip last year was $4.75. To support this claim, she sent the IRS a random
sample of 22 credit card receipts showing her bar tips. When the IRS got the receipts, they computed the
sample average and found it to be $5.25 with a sample standard deviation of $1.15. do these receipts
indicate that the average tip Maureen received last year was more than $4.75? Use a 1% significance level.