AP Statistics
Chapter 13
Comparing Two Means
NAME:___________________________________
1.) In a study of cereal leaf beetle damage on oats, researchers measured the number of beetle larvae
per stem in small plots of oats after randomly applying one of two treatments: no pesticide, or
malathion, a new pesticide. The data appear roughly normal. Here are the summary statistics.
Group
1
2
Treatment
Control
Malathion
n
13
14
x
3.47
1.36
s
1.21
0.52
Is there significant evidence at the 1% level that malathion reduces the mean number of larvae per
stem?
2.) The Effect of Logging How badly does logging damage tropical rainforests? One study
compared forest plots in Borneo that had never been logged with similar plots nearby that had been
logged 8 years earlier. The study found that the effects of logging were somewhat less severe than
expected. Here are the data on the number of tree species in 12 unlogged plots and 9 logged plots:
Unlogged
Logged
22
17
18
4
22
18
20
14
15
18
21
15
13
15
13
10
19
12
13
19
15
Give a 90% confidence interval for the difference in mean number of species between unlogged and
logged plots.
3.) Country A and Country B have been competing in the 200-meter dash in the Olympics for many
years. A SRS of 200 meter running times for both countries is listed below:
Country A
Country B
x
24.52
24.6
s
0.76
0.82
n
13
13
a.) Is there significant evidence to conclude that there is a difference between the average speed of the
two groups? Give appropriate statistical justification.
b.) Construct a 95% confidence interval for the difference between the average speeds of the two
groups. Explain how this interval confirms or contradicts your conclusion in part a.
4.) Charles Darwin was interested in whether there was any difference in the heights of plants that
were cross-fertilized or self fertilized. The data below shows the height in inches of plants grown in 15
pairs for a fixed period of time. One member of each pair was cross fertilized, and the other was selffertilized.
Pair
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Cross-fertilized
23.5
12.0
21.0
22.0
19.1
21.5
22.1
20.4
18.3
21.6
23.3
21.0
22.1
23.0
12.0
Self Fertilized
17.4
20.4
20.0
20.0
18.4
18.6
18.6
15.3
16.5
18.0
16.3
18.0
12.8
15.5
18.0
What conclusions could Darwin have drawn from this data? Justify your answer by using the proper
inference test.