School

Ryerson University
Department

Quantitative Methods

Course Code

QMS 202

Professor

Jason Chin- Tiong Chan

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

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

www.notesolution.com

QMS202-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

Âµ

â‰

2

Âµ

z

= -1.8137025

p

= 0.06972353

1

x

= 5300

2

x

= 5760

1

n

= 45

2

n

= 50

Winter2011 2

www.notesolution.com

QMS202-Business Statistics II Chapter11

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

critical

z

= 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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