Two Sample Tests
Directions: Set up the hypothesis. Write the formula. Use the calculator to find the test statistic and p-val. .
1.
David E. Brown is an expert in wildlife conservation. In his book, he recorded the weights of adult grey wolves from two regions in Old Mexico. Find and interpret the 85% confidence interval for the difference in weights of the wolves from the Chihuahua region and the Durango region.
86
80
75
68
Chihuahua (
91
71

1
)
70
74
79
64
68
68
72
59
79
63
Durango (
68
66
77

2
)
58
89
54
62
71
55
59
68
67
2.
A credit card watchdog group claims that there is a difference in the mean credit card debts of households in New York ( 
1
) and Texas ( 
2
). The mean credit card debt in New York was $4446.25 with a standard deviation of $1045.70 while the mean for Texas was $4567.24 with a standard deviation of
$1361.95. In each state 250 households were sample. Test using a 5% level of significance.
3.
Based on information from Harper’s Index, 78 out of a random sample of 100 American adults claim that they would donate a loved one’s organs after death. However, out of a random sample of 100 adult
Americans, only 20 claim that they would donate their own organs after death. Does this information indicate that the proportion of adult Americans (p
1 the proportion from the magazine survey(p
2
)? Use
) who would donate a loved one’s organs is higher than
 
0.01
.
4.
Paramedics in a large city say they need more staff at night because they get more emergency calls then.
A random sample of seven days showed that the paramedics received the following # of calls during the day and night. Use a 1% level of significance to test the claim that there are more calls during the night.
# Day calls (

1
# Night calls(

2
)
)
65
72
54
81
81
85
67
80
75
88
83
82
79
56
5.
A pharmaceutical company guarantees that its new drug reduces systolic blood pressure. The table shows the systolic blood pressures of eight patients before taking the new drug and two hours after taking the drug. Test at a 5% level of significance.
Before
After
201 171 186 162 165 167 175 148
192 165 167 155 148 144 152 134

6.
Six sets of identical twins were randomly selected from a population of identical twins. One child was taken at random form each pair to participate in a program designed to promote creative thinking. The other child from each pair was part of the control group that did not participate in the program. Higher scores indicate better performance in creative problem solving. Does the data support the claim that the program of the experimental group did promote creative problem solving?
Twin Pair
Experimental
Control
A
53
39
B
35
21
C
12
5
D
33
21
E
25
18
F
47
42
7.
A study of 150 randomly selected occupants in passenger cars and 200 randomly selected occupants in pickup trucks shows that 86% of occupants in passenger cars and 74% of occupants in pickup trucks wear seat belts. At a 10% level of significance, can you support the claim that the proportion of occupants in passenger cars (p
1
) who wear their seat belt is higher than the proportion of occupants in trucks (p
2
)?
8.
A sociologist claims that children ages 6-17 spent more time watching tv in 1981 than children ages 6-17 do today. At a 5% level of significance, can you support the sociologist’s claim.
# hours (1981) 2 2.5 2.1 2.3 2.1 1.6 2.6 2.1 2.4 2.1 2.1 1.5
# hrs (present) 2.9 1.8 0.9 1.6 2 1.7 2.5 1.1 1.6 1.4 1.7 1.9
9.
Two independent random samples were taken at two large high schools to determine the difference in the proportions of students who had jobs outside of school. The sample of 75 North High students indicated that 60% of them had jobs outside of school while the sample of 40 South High students indicated that
68% of them had jobs outside of school. Construct and interpret a 95% confidence interval for the difference in proportions of working students at each of these high schools based on these samples.
10.
An investigator wishes to study television viewing habits among teenagers in a particular suburb. She knows that the standard deviation for the number of hours watched per day by all teenagers is 2.9 hours. How large of a simple random sample much be taken to estimate the population mean with a margin of error of 1 hour at the 99% confidence level?