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Lecture

# Chapter 11 - Part One

24 Pages
188 Views

Department
Quantitative Methods
Course Code
QMS 202
Professor
Jason Chin- Tiong Chan

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Chapter11 Two-Sample Tests and
One-Way ANOVA (Part I)
Outcomes:
1. Conduct a test of hypothesis for two independent population means
- Use z-test when
1
Ïƒ
and
2
Ïƒ
are known
- Use pooled-variance t test when
1
Ïƒ
and
2
Ïƒ
are unknown but equal
- Use separate-variance t test when
1
Ïƒ
and
2
Ïƒ
are unknown and
unequal
2. Conduct a test of hypothesis for paired or dependent observations,
using the paired t-test
3. Conduct a test of hypothesis for two population proportions
using the z test
4. List the characteristics of the F distributions
5. Conduct a test of hypothesis to determine whether the variances
of two populations are equal, using the F Test
6. Discuss the general idea of Analysis of Variance (ANOVA) and its
assumptions
7. Conduct the F Test when there are more than two means
8. Discuss multiple comparisons: The Tukey-Kramer procedure
9. Conduct Leveneâ€™s Test for Homogeneity of Variance
Winter2011 1
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Example1
Ryerson Car magazine is comparing the total repair costs incurred during
the first three years on two sport cars, The R123 and the S456. Random
samples of 45 R123 cars are \$5300 for the first three years. For the 50
S456 cars, the mean is \$5760. Assume that the standard deviations for the
two populations are \$1120 and \$1350, respectively. Using the 5%
significance level, can we conclude that such mean repair costs are
different for these two types of cars?
Calculator Output
2-Sample z Test
1
Âµ
â‰
2
Âµ
z
= -1.8137025
p
= 0.06972353
1
x
= 5300
2
x
= 5760
1
n
= 45
2
n
= 50
Winter2011 2
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Step1
Let
1
Âµ
be the population mean repair cost for sport car R123
Let
2
Âµ
be the population mean repair cost for sport car S456
Step2
21
:
ÂµÂµ
=
o
H
21
:
ÂµÂµ
â‰
A
H
Step3
Level of significance = 0.05/2=0.025
Step 4
2-sample mean z test
Step5
statistic
z
= -1.8137
= p-value =
0.06972353
Step6
Since the p-value > 0.05, do not reject the null hypothesis.
There is not enough evidence to conclude that such mean repair costs are
different for these two types of cars
Winter2011 3
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Description
QMS202-Business Statistics II Chapter11 Chapter11 Two-Sample Tests and One-Way ANOVA (Part I) Outcomes: 1. Conduct a test of hypothesis for two independent population means -Use z-test when 1 and 2 are known - Use pooled-variance t test when 1 and 2 are unknown but equal - Use separate-variance t test when 1 and 2 are unknown and unequal 2. Conduct a test of hypothesis for paired or dependent observations, using the paired t-test 3. Conduct a test of hypothesis for two population proportions using the z test 4. List the characteristics of the F distributions 5. Conduct a test of hypothesis to determine whether the variances of two populations are equal, using the F Test 6. Discuss the general idea of Analysis of Variance (ANOVA) and its assumptions 7. Conduct the F Test when there are more than two means 8. Discuss multiple comparisons: The Tukey-Kramer procedure 9. Conduct Levenes Test for Homogeneity of Variance Winter2011 1 www.notesolution.comQMS202-Business Statistics II Chapter11 Example1 Ryerson Car magazine is comparing the total repair costs incurred during the first three years on two sport cars, The R123 and the S456. Random samples of 45 R123 cars are \$5300 for the first three years. For the 50 S456 cars, the mean is \$5760. Assume that the standard deviations for the two populations are \$1120 and \$1350, respectively. Using the 5% significance level, can we conclude that such mean repair costs are different for these two types of cars? Calculator Output 2-Sample z Test 1 2 z = -1.8137025 p = 0.06972353 x1 = 5300 x = 5760 2 n1 = 45 n 2 = 50 Winter2011 2 www.notesolution.com
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