MGMT2263
Worksheet
#4
1)
An auto manufacturer with 2 plants wanted to compare the
percentage of scrap widgets between them. They collected samples at the plants.
These were the results:
|
Sample size |
Number of scrap widgets |
|
|
Plant #1 |
500 |
6 |
|
Plant #2 |
500 |
8 |
Is there any
significant difference in the percentage of scrap widgets at the 2 plants? Test
at 5%. (Z = -0.5383; conclude no significant difference)
2)
Construct a 95% confidence interval of the difference of
proportions between plant #2 and plant #1. Interpret what it means. (-1.1% <
p2 – p1 < 1.9% ; We are 95% confident that the
percentage of scrap widgets for plant #2 ranges from 1.1% less to 1.9% more
than plant #1)
3)
Suppose they want to see if the difference in the
percentage of scrap chips between Plant #2 and Plant #1 was significantly more
than 1%. Use a p-value approach. (p-value = 0.791;
conclude the spread is not more than 1%)
4)
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)
5)
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.
6)
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 = 42.1; 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 = 0.81; conclude no significant
difference between the salespeople)
d)
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?
From the textbook
9.77 (page
305)
10.12 and 10.13 (just the pairwise
comparisons at a 5% level of significance) (page 330)
10.19 (page
337)