The Richard Manufacturing Company
produces custom wooden crates that are sold to shipping companies worldwide.
Each crate is assembled by skilled line-operators. Each operator is expected to
produce, on the average, the same number of finished units per day. Data for
two operators was collected for a period of a week (6 days total) and resulted
in the following data.
Day
|
Operator 1 |
Operator 2 |
|
Monday |
108 |
106 |
|
Tuesday |
115 |
118 |
|
Wednesday |
118 |
116 |
|
Thursday |
116 |
115 |
|
Friday |
110 |
114 |
|
Saturday |
115 |
112 |
ITEM 2
|
Supplier 1 |
Supplier 2 |
Supplier 3 |
Supplier 4 |
|
18.5 |
26.3 |
20.6 |
25.4 |
|
24.0 |
25.3 |
25.2 |
19.9 |
|
17.2 |
24.0 |
20.8 |
22.6 |
|
19.9 |
21.2 |
24.7 |
17.5 |
|
18.0 |
24.5 |
22.9 |
20.4 |
a) Construct the ANOVA table for this
problem.
b)
Can
we conclude whether or not the population variances differ? Conduct the
required test of hypothesis using a 5% level of significance. Based on the
conclusion of this test, is it appropriate to conduct ANOVA? Discuss briefly.
c)
Is
the mean tensile strength different amongst the four suppliers? Conduct the
required test of hypothesis using a 5% level of significance.
d)
Is
Tukey’s assessment useful? Base your answer on your conclusion reached in part
c). If you conclude that this assessment is useful, which means are
significantly different using a 5% level of significance?
e) Calculate a 95% simultaneous
confidence interval for the difference in mean tensile strength between the
fabric from Supplier #2 and Supplier #1. Why does this support the results of
the hypothesis test in part c?
ITEM
3
A study is being conducted by a major marketing
research firm with regard to the number of full-page advertisements run in
nationally circulated monthly magazines. They are particularly interested in
two of these magazines, A and B. A random sample of monthly issues was selected
and the number of full-page ads was counted and resulted in the following data.
|
A |
17 |
26 |
18 |
16 |
15 |
23 |
20 |
|
B |
8 |
9 |
24 |
12 |
10 |
a) Assuming the data is normally
distributed, is there any difference between the population variances of the
two magazines? Conduct the required test of hypothesis at a 5% level of
significance.
b) Based on the results of part a),
what specific means difference test should be conducted? Explain your answer
briefly but do not conduct the test at this point.
c) Using the test outlined in part b),
conduct the required test of hypothesis to assess if there is a difference in
the mean number of full-page ads in the two magazines. Assume no level of
significance in conducting your test.
d) Would your test conclusion change in
part c) if you had used a 1% level of significance to conduct the test? Discuss
why or why not.
e) Calculate a 95% confidence interval
for the difference in the mean number of full-page ads in the two magazines. If
this interval were used to test the hypothesis in part c based on a 5% level of
significance, what conclusion would be reached and why?
Reconsider
the problem setup and the data from ITEM 3.
a)
If
the data can no longer be considered to have been drawn from normally
distributed populations, what non-parametric test should be conducted in order
to address the question of whether or not the volume of full-page ads differ
between the two magazines? Briefly explain.
b)
Using
the test method outlined in part a), conduct the required non-parametric
analysis. Use a 5% level of significance in the test.
A marketing research analyst has been hired by
a major consumer electronics manufacturer to study the difference in age usage
of MP3 systems. The two groups studied were those 25 years old
and younger and those over 25 years of age. In the group of individuals 25
years and younger a sample of 1200 individuals were surveyed and 900 expressed
that they used an MP3 system on a regular basis. The group of
individuals that were over 25 years of age was made up of 1500 individuals and
900 of them expressed that they used an MP3 system on a regular
basis. Using this information answer the following questions.
a) Can we conclude that there is more
than a 10% greater usage of MP3 systems in the 25 year old or younger group
when compared to the over 25 year age group? Conduct the required test of
hypothesis using a 5% level of significance.
b) Estimate a P-value for the test
conducted in part a). Does this value support the test outcome reached in part
a)? Discuss briefly.
c) Calculate a 95% confidence interval
estimate for the difference in rates of MP3 usage between the two
groups.
ITEM
6
A focus
group of 10 IT professionals were asked to compare two operating systems on a
scale from 1 to 10 with 10 being best. These were the results:
|
Person |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
|
System
A |
5 |
7 |
7 |
4 |
6 |
7 |
7 |
7 |
7 |
6 |
|
System
B |
8 |
7 |
6 |
7 |
6 |
8 |
9 |
8 |
8 |
8 |
Is system B
rated significantly better than system A? Test at a 5% level of significance.
ITEM
7
An
educational researcher wanted to determine if the average grade 12 achievement
score was significantly higher for one region than for a second region which
has a higher percentage of students whose second language is English. These
were the results:
|
Region 1 |
Region 2 |
|
|
Mean |
67.5 |
64.4 |
|
Standard deviation |
7.8 |
8.2 |
|
Sample size |
100 |
100 |
a)
Test
the hypothesis without specifying a level of significance.
b)
Construct
a 97.5% confidence interval of the average difference in the scores between the
2 regions. Round the margin of error to 1 decimal.
c)
Test
the hypothesis that the average grade in Region 2 is more than 1 mark less than
the average grade in Region 1 at a 3.92% level of significance.
ITEM
8
A tourist
magazine wanted to compare inner city hotels and those in the suburbs to see if
there was any significant difference in average daily rates. It sampled 12 from
each type. These were the results:
|
Downtown |
597 |
400 |
602 |
309 |
292 |
458 |
452 |
484 |
492 |
753 |
421 |
777 |
|
Suburbs |
429 |
531 |
475 |
519 |
479 |
458 |
469 |
499 |
468 |
482 |
435 |
472 |
Analysis of
the data indicates both groups are normally distributed but do not share equal
variances.
a)
Test
at a 5% level of significance.
b)
Estimate
the range of the p-value. If a level of significance had not been chosen, what
conclusion be reached and why?
c)
Construct
a 95% confidence interval of the average difference in average daily rates
between downtown and suburban hotels. Round the margin of error to the nearest
cent. If this interval were used to test the hypothesis in part a, why would
the same conclusion be reached?