Discuss the following:
1. Which national park has more bears? Random samples of plots of ten square miles were taken in different parts of Yellowstone National Park, Yosemite National Park and Glacier National Park. The bear counts per square mile were recorded as shown below:
|
Yellowstone
|
Yosemite
|
Glacier
|
|
2
|
3
|
8
|
|
1
|
0
|
3
|
|
4
|
4
|
5
|
|
2
|
1
|
8
|
We want to test whether there is a difference in the mean number of bear per ten square mile plot in these three different parks using a 5% level of significance.
a. State the hypotheses.
b. Calculate the SSTOTAL, SSBETWEEN, and SSWITHIN.
c. Using these values, create the summary table for your ANOVA test.
d. From the table, state the test statistic and p-value, and state your conclusion at the 5% level of significance.
2. What affects grade point average? Does GPA depend on gender? Does GPA depend on class (freshman, sophomore, junior, senior)? In a study, the following GPAs were collected from random samples of college students. There are four values in each cell:
|
|
Freshmen
|
Sophomore
|
Junior
|
Senior
|
|
Male
|
3.2, 3.6, 3.8, 3.5
|
3.7, 3.3, 3.6, 2.6
|
3.3, 3.6, 2.6, 2.4
|
2.3, 3.5, 3.9, 2.9
|
|
Female
|
3.8, 3.6, 3.5, 3.1
|
2.9, 3.8, 3.1, 3.2
|
2.3, 2.5, 2.9, 3.5
|
3.0, 2.1, 2.8, 2.7
|
a. List the factors and the number of levels for each factor.
b. Suppose the test statistic and p-value for the interaction term are 0.43 and 0.736, respectively. Determine if there is any evidence of interaction between the two factors at the 5% level of significance.
c. Suppose the test statistic and p-value for the class factor are 3.32 and 0.037, respectively. Determine if there is any evidence of a difference in mean GPA based on class at the 5% level of significance.
d. Suppose the test statistic and p-value for the gender factor are 1.26 and 0.273, respectively. Determine if there is any evidence of a difference in mean GPA based on gender at the 5% level of significance.
3. A new medicinal drink is thought to help people stop smoking cigarettes. To test this, a random sample of 18 subjects agreed to drink one drink once a day for a month. Data is collected for these 18 subjects based on the number of cigarettes per day prior to starting the program, and the number of cigarettes per day after starting the program. Below is the data for these 18 subjects:
|
Subject
|
Number before program
|
Number after program
|
|
1
|
24
|
24
|
|
2
|
25
|
19
|
|
3
|
14
|
2
|
|
4
|
17
|
17
|
|
5
|
25
|
29
|
|
6
|
30
|
19
|
|
7
|
18
|
7
|
|
8
|
15
|
18
|
|
9
|
11
|
1
|
|
10
|
20
|
5
|
|
11
|
30
|
12
|
|
12
|
40
|
21
|
|
13
|
26
|
28
|
|
14
|
38
|
17
|
|
15
|
10
|
0
|
|
16
|
32
|
15
|
|
17
|
18
|
4
|
|
18
|
24
|
18
|
Using a sign test for matched pairs at the .01 level of significance, we will test the claim that the number of cigarettes smoked per day was less after the program.
a. State the null and alternative hypotheses.
b. Compute the sample test statistic.
c. Find the p-value.
d. State the conclusion at the .01 level of significance.
4. Two different methods are used to help children learn how to spell. Each child was given 60 words to spell, and it was noted how many words each child spelled correctly. Here are the counts for both methods:
|
Method A
|
28
|
35
|
19
|
41
|
37
|
31
|
38
|
40
|
25
|
27
|
36
|
43
|
|
Method B
|
42
|
33
|
26
|
24
|
44
|
46
|
34
|
20
|
48
|
39
|
45
|
|
Use a rank-sum test at the 0.05 level of significance to test the claim that there is no difference between the distributions for each method.
a. State the null and alternative hypotheses.
b. Compute the sample test statistic.
c. Find the p-value.
d. State the conclusion at the .05 level of significance.
5. A math class is given a difficult test and they score poorly on the test. The instructor asks each individual student approximately how many minutes they studied for the test to see if there is some correlation between how long they studied and their test score. Here is the data for seven students:
|
Student
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
|
Minutes studied
|
60
|
85
|
78
|
90
|
93
|
45
|
51
|
|
Test score
|
78
|
42
|
68
|
53
|
62
|
50
|
76
|
Use a Spearman rank correlation test to determine if there is significant correlation between these two variables.
a. State the null and alternative hypotheses.
b. Compute the sample test statistic.
c. Find the p-value.
d. State the conclusion at the .05 level of significance.