STAT177 homework sheet #8
A school board wanted to compare average grades between four schools in different regions of its jurisdiction. Ten grades were randomly selected from each school. The results were:
|
49 |
72 |
59 |
65 |
80 |
70 |
86 |
78 |
84 |
53 |
|
|
School B |
58 |
92 |
76 |
60 |
80 |
50 |
52 |
54 |
57 |
80 |
|
School C |
66 |
98 |
97 |
76 |
88 |
69 |
86 |
62 |
75 |
61 |
|
School D |
96 |
82 |
89 |
92 |
74 |
76 |
93 |
94 |
71 |
81 |
1)
What is the
appropriate test? (one-way ANOVA)
2)
Is there any
significant difference in the average grade between the schools? Test at 5%.
(p-value = 0.01; conclude there is a significant difference between at least 2
of the schools)
3)
Judging by the results
of the analysis, between which schools is there a significant difference?
(School B and School D)
A factory wanted to compare production between its day, afternoon and night shifts. It has 5 lines. They sampled 5 hours worth of production from each line and measured the number of widgets built per hour. These were the results:
|
|
Day |
Afternoon |
Night |
|
Line 1 |
31 |
25 |
35 |
|
Line 2 |
33 |
26 |
33 |
|
Line 3 |
28 |
24 |
30 |
|
Line 4 |
30 |
29 |
28 |
|
Line 5 |
28 |
26 |
27 |
4)
What is the
appropriate test? (2-way ANOVA)
5)
Is there any
significant difference in production between the shifts? Test at 5%. (p-value =
0.028; conclude there is a significant difference between at least 2 of the
shifts)
6)
Between which shifts
is there a significant difference? (Afternoon and night shift)
7)
Is there any
significant difference in production between the lines? (p-value = 0.276;
conclude no significant difference between the lines)
A potato chip manufacturer conducted a focus group with 10 participants
to see which of 3 new brands they liked on a scale of 1 to 10 where 1 means
poor and 10 means excellent. These were the results:
|
|
Brand A |
Brand B |
Brand C |
|
Person #1 |
6 |
8 |
8 |
|
Person #2 |
10 |
7 |
6 |
|
Person #3 |
6 |
5 |
4 |
|
Person #4 |
7 |
8 |
3 |
|
Person #5 |
9 |
7 |
4 |
|
Person #6 |
8 |
7 |
6 |
|
Person #7 |
9 |
4 |
6 |
|
Person #8 |
8 |
4 |
4 |
|
Person #9 |
7 |
4 |
1 |
|
Person
#10 |
9 |
9 |
1 |
8)
What is the
appropriate test for the data? (Friedman)
9)
Based on the results
of this focus group, is there any significant difference in how people like
these new brands? (p-value = 0.01; conclude that at least 2 brands are rated
differently)
10)
Which brand has the
highest rating? Which the lowest? (Brand A the highest; Brand C the lowest)
A
company tested 3 market research firms to see which of them had the highest
completion rates for its survey. In 10 separate hours, these were the average
completion rates for each firm:
|
Firm A |
Firm B |
Firm C |
|
2.6 |
3.6 |
4.6 |
|
2.2 |
3.9 |
3.9 |
|
2.9 |
3.8 |
4.2 |
|
3.3 |
3.7 |
3.9 |
|
3.3 |
2.7 |
4.8 |
|
3.4 |
3.7 |
4.3 |
|
2 |
3.6 |
5 |
|
2.6 |
2.6 |
4 |
|
3.3 |
2.9 |
3.6 |
|
2.2 |
2.7 |
3.6 |
11) Is there any significant different in the average
completion rates per hour of the 3 firms? Test at a 5% level of significance.
(p-value = 0; conclude at least 2 firms completion rates are different)
12) Between which firms are the hourly completion rates
significantly different at a 5% level of significance? Based on the results,
which firm should be chosen? (All 3 firms are significantly different; choose
Firm C)
From the text, read:
Chapter 6, pages 102-115 (to end of Friedman test)