STAT217 Worksheet
#4
Question 1
A real estate company wanted to compare average sales among its three locations. For a randomly selected month, the number of sales for each salesperson from each location was recorded. The results were:
|
Office A |
2 |
5 |
6 |
3 |
||
|
Office B |
1 |
4 |
3 |
3 |
2 |
2 |
|
Office C |
2 |
2 |
2 |
3 |
1 |
a) If it can be assumed that the data is normally distributed and that the three offices share the same standard deviation, is there any significant difference in the average sales of the three offices? Test at a 5% level of significance. (F = 3.2344; conclude no significant difference in the average sales of the three offices)
b) Conduct Tukey’s test on the pair of offices with the largest and smallest sample means at a 5% level of significance. Why does it support the results of part a?
c) Construct a 95% simultaneous confidence interval of the average difference between the offices used in part b. Why does this interval support the results of part a? (-0.1595 < m1 - m3 < 4.1595)
Question 2
A school board wanted to compare average grades between four schools in different regions of its jurisdiction. Eight grades were randomly selected from each school The results were:
|
School A |
49 |
72 |
59 |
65 |
80 |
70 |
86 |
78 |
|
School B |
58 |
92 |
76 |
60 |
80 |
50 |
52 |
54 |
|
School C |
66 |
98 |
97 |
76 |
88 |
69 |
86 |
62 |
|
School D |
96 |
82 |
89 |
92 |
74 |
76 |
93 |
94 |
Analysis of the data indicates that each school’s grades are normally distributed and they share a common standard deviation.
a) Is there any significant difference in the average grades of the four schools? Test at a 5% level of significance. (F = 4.7792. Conclude that the average grades for at least 2 schools are significantly different)
b) Between which schools is there a significant difference? Why is this consistent with the results of ANOVA? (B and D)
c) What is the estimate of the common standard deviation among the four schools? (12.753)
d) Construct a 95% simultaneous confidence interval of the average difference between school D and school B. Does the confidence interval seem to be consistent with the results of the hypothesis test? (4.3909 < m(D) - m(B) < 39.1091)
e) It was stated above that the school grades share a common standard deviation. Conduct the appropriate test at a 5% level of significance to confirm this. (KW = 1.98; conclude no significant difference in variances.)
Question 3
In a survey, salespeople for a company were asked to estimate the average amount of time each week they do various tasks. Here were the results for 6 of the salespeople:
|
|
Paperwork |
Handling returns |
Meeting with
clients |
|
Person
#1 |
32 |
34 |
52 |
|
Person
#2 |
22 |
32 |
48 |
|
Person
#3 |
27 |
27 |
46 |
|
Person
#4 |
19 |
37 |
52 |
|
Person
#5 |
13 |
34 |
53 |
|
Person
#6 |
24 |
42 |
50 |
Analysis of the data showed it to be normally distributed with the tasks sharing a common standard deviation.
a) Is there any significant difference in the average amount of time spent on each task? Test at a 5%. level of significance (F = 42.079; conclude the average time is significantly different for at least 2 of the tasks)
b) Based on Tukey’s test, which pairs of tasks are significantly different? (All 3 tasks are significantly different)
c) Is there any significant difference in the average amount of time spent by the salespeople on these tasks? Test at 5%.(F = 0.8076; conclude no significant difference between the salespeople)
a) Construct a 95% simultaneous confidence interval of the average difference between handling returns and doing paperwork, rounding the limits to the nearest minute. Why is this interval consistent with the ANOVA results?
(3 < m(returns) - m(paperwork) < 20)
Question 4
Gross annual incomes of realtors from 3 cities were compared. Seven realtors were sampled from each city. These were the results (rounded to nearest thousand):
|
City 1 |
City 2 |
City 3 |
|
98 |
82 |
64 |
|
86 |
92 |
74 |
|
76 |
90 |
76 |
|
66 |
99 |
86 |
|
30 |
74 |
67 |
|
76 |
61 |
80 |
|
85 |
59 |
82 |
No assumptions about the normality of the data were made. Is there any significant difference in the average gross annual incomes of realtors from the different cities? Test at a 5% level of significance. (chi-square = 0.3915; conclude no significant difference)
Question 5
In a study for a museum, people were asked to rate six different exhibits on a scale from 1 to 10, 10 being the best. Suppose that for a sample of 10 people, these were the results:
|
|
A |
B |
C |
D |
E |
F |
|
Person
#1 |
8 |
3 |
2 |
3 |
3 |
7 |
|
Person
#2 |
5 |
5 |
5 |
1 |
9 |
1 |
|
Person
#3 |
8 |
10 |
8 |
7 |
10 |
8 |
|
Person
#4 |
4 |
5 |
5 |
3 |
6 |
2 |
|
Person
#5 |
10 |
9 |
9 |
7 |
10 |
6 |
|
Person
#6 |
10 |
9 |
2 |
5 |
6 |
4 |
|
Person
#7 |
5 |
6 |
8 |
8 |
2 |
3 |
|
Person
#8 |
8 |
6 |
6 |
8 |
7 |
9 |
|
Person
#9 |
10 |
10 |
10 |
10 |
10 |
10 |
|
Person
#10 |
6 |
6 |
5 |
7 |
8 |
6 |
Is there any significant difference in how people rank the 6 exhibits? Test at a 5% level of significance. (chi-square = 6.5143; conclude no significant difference among exhibits)
From the textbook
Chapter 9 review exercises Q2 (page 539)
Section 12-5 Q1 (page 718) and Q9 (page 721)