Chapter 10_Tutorial_W24
pdf
keyboard_arrow_up
School
University of Windsor *
*We aren’t endorsed by this school
Course
2910
Subject
Mathematics
Date
Apr 3, 2024
Type
Pages
4
Uploaded by DukeMouseMaster1019
Department of Mathematics and Statistics
STAT2910-01: Statistics for Sciences
Faculty of Science
University of Windsor
Tutorial for Chapter 10
Exercise 1.
The manufacturer of a particular battery pack for laptop computers claims its battery pack can function
for 8 hours, on average, before having to be recharged. A random sample of 16 battery packs was selected
and tested.
The mean functioning time before having to be recharged was 7.2 hours with a standard
deviation of 1.9 hours.
(a)
Assuming the distribution of functioning times is approximately normal, find a 95% confidence in-
terval for the true average functioning time before needing to be recharged.
(b)
Interpret the interval in the previous question.
(c)
Based on the interval calculated above, can the manufacturer’s claim be rejected? Justify your answer
Exercise 2.
The public relations officer for a particular city claims the average monthly cost for childcare outside the
home for a single child is $600. A potential resident is interested in whether the claim is correct. She
obtains a random sample of 14 records and computes the average monthly cost of this type of childcare
to be $589 with a standard deviation of $40. Perform the appropriate test of hypothesis for the potential
resident using
α
= 0
.
01.
Exercise 3.
An experiment to determine the efficacy of using 95% ethanol or 20% bleach as a disinfectant in removing
bacterial and fungal contamination when culturing plant tissues was repeated 15 times for each disinfec-
tant. The plant tissue being cultured was sweet potato: Five cuttings per plant were placed on a petri
dish for each disinfectant and stored at 25 C for four weeks. The observation reported was the number
of uncontaminated eggplant cuttings after the four-week storage.
95% Ethanol
20% Ethanol
Sample Size
15
15
Sample Mean
3.85
4.92
Sample Variance
2.75
0.18
(a)
Is it reasonable to assume that the underlying variances are equal? Justify your conclusion.
(b)
Using the information from the previous question, are you willing to conclude that there is a significant
difference in the mean numbers of uncontaminated eggplants for the two disinfectants tested?
Exercise 4.
Assume that the population distributions of ages (in years) of students at two different universities in On-
tario are normal with equal variances. Two random samples, drawn independently from the populations,
showed the following statistics:
n
1
= 10
,
¯
x
1
= 25
, s
2
1
= 4;
n
2
= 9
,
¯
x
2
= 24, and
s
2
2
= 9. Construct and
interpret a 99% confidence interval for the true difference in average ages of students at each university.
1
Exercise 5.
A computer laboratory manager was in charge of purchasing new battery packs for her lab of laptop
computers.
She narrowed her choices to two models that were available for her machines.
Since the
models cost about the same, she was interested in determining whether there was a difference in the
average time the battery packs would function before needing to be recharged. She took two independent
random samples and computed the following summary information:
Battery Pack Model 1
Battery Pack Model 2
Sample Size
9
9
Sample Mean
5 hours
5.5 hours
Standard Deviation
1.5 hours
1.3 hours
(a)
Perform the appropriate test of hypotheses to determine whether there is a significant difference in
average functioning time before recharging between the two models of battery packs.
Test using
α
= 0
.
05.
(b)
Is it reasonable to assume equality of variances in this problem? Justify your answer.
(c)
Use
α
= 0
.
05 to test the hypothesis that the two population variances are equal.
Exercise 6.
Do government employees take longer coffee breaks than private sector workers? That is a question that
interested a management consultant. To examine the issue, he took a random sample of ten government
employees and another random sample of ten private sector workers and measured the amount of time
(in minutes) they spent in coffee breaks during the day. The results are listed below.
Government Employees
Private-Sector Workers
23
25
18
19
34
18
31
22
28
28
33
25
25
21
27
21
32
20
21
16
(a)
Do these data provide sufficient evidence at the 5% significance level to support the consultant’s
question Justify your conclusion?
(b)
Estimate with 95% confidence the difference between the two groups in coffee break mean time
(c)
Explain what the interval estimate tells you.
Exercise 7.
Let
µ
denote the true average number of minutes of a television commercial.
Suppose the hypotheses
H
0
:
µ
= 4
.
8
Vs.
H
a
:
µ
̸
= 4
.
8 are tested. Assuming the commercial time is normally distributed, give
the appropriate rejection region for each of the following sample sizes and significance levels.
(a)
n
= 6
, α
= 0
.
01
2
(b)
n
= 12
, α
= 0
.
05
(c)
n
= 20
, α
= 0
.
05
(d)
n
= 23
, α
= 0
.
1
Exercise 8.
A consumer was interested in determining whether there is a significant difference in the price charged
for tools by two hardware stores. The consumer selected five tools and recorded the price for each tool in
each store. The following data were recorded:
Store
1
2
3
4
5
1
$32
.
00
$3
.
95
$1
.
50
$2
.
95
$4
.
00
2
$30
.
00
$2
.
95
$1
.
50
$2
.
45
$5
.
00
d
i
2
1
0
0.5
-1
(a)
Are the samples independent? Justify your answer.
(b)
Perform the appropriate test of hypothesis to determine whether there is a significant difference, on
average, in the price of tools between the two stores. Use
α
= 0
.
05.
Exercise 9.
Five soft drink bottling companies have agreed to implement a time management program in hopes of
increasing productivity (measured in cases of soft drinks bottled per hour). The number of cases of soft
drinks bottled per hour before and after the implementation of the program are listed below:
1
2
3
4
5
Before
500
475
525
490
530
After
510
480
525
495
533
(a)
State the appropriate null and alternative hypotheses to test whether the time management has been
effective in increasing productivity
(b)
Calculate the value of the test statistic.
(c)
Set up the appropriate rejection region for the hypotheses above, assuming
α
= 0
.
05.
(d)
What is the appropriate conclusion? Justify your answer.
(e)
Find the approximate p-value.
Exercise 10.
A customer service representative was interested in comparing the average time (in minutes) customers
are placed on hold when calling Gaz Metropolitan and Hydro-Quebec, both in Quebec. The representative
obtained two independent random samples and calculated the following summary information:
Gaz Metropolitan
Hydro-Quebec
Sample Size
9
12
Sample Mean
3.2 min
2.8 min
Sample Standard deviation
0.5 min
0.7 min
3
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
Assume the distributions of time a customer is on hold are approximately normal. Use
α
= 0
.
10to
test the hypotheses that the two population variances are equal.
Exercise 11.
A customer was interested in comparing the top speed (in kilometers per hour) of two models of snow-
mobiles. The customer selected two independent random samples of the snowmobiles and calculated the
following summary information:
Model A
Model B
Sample Size
8
9
Sample Mean
90
84
Sample Standard Deviation
3
5
Assume the distribution of top speeds is approximately normal.
(a)
State the appropriate null and alternative hypotheses to test whether there is a significant difference
between the two models of snowmobiles in average top speed.
(b)
Calculate the value of the test statistic.
(c)
Set up the appropriate rejection region for the hypotheses above assuming
α
= 0
.
05.
(d)
What is the appropriate conclusion? Be sure to justify your answer.
(e)
Use
α
= 0
.
05 to test the hypothesis that the two population variances are equal.
4