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 II)

Outcomes:

1. Conduct a test of hypothesis for two independent population means

- Use z-test when

1

σ

and

2

σ

are known

- Use pooled-variance t test when

1

σ

and

2

σ

are unknown but equal

- Use separate-variance t test when

1

σ

and

2

σ

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 Levene’s Test for Homogeneity of Variance

Winter2011 1

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QMS202-Business Statistics II Chapter11

Characteristics of F distribution

1. There is a “family” of F distributions. Each member of the family is

determined by two parameters

i. the degree of freedom in the numerator

ii. the degree of freedom in the denominator

2. The F distribution is continuous

This means that it can assume an infinite number of values between 0 and

positive infinity

3. The F distribution cannot be negative

The smallest value F can assume is 0

4. It is positively skewed

The long tail of the distribution is to the right-hand side. As the number of degrees

of freedom increases in both numerator and denominator, the distribution

approaches a normal distribution

5. It is asymptotic

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QMS202-Business Statistics II Chapter11

Question#1

Ryerson Limos offers limousine service from the city hall in Toronto, Ontario, to the

Toronto International Airport, John, president of the company, is considering two

routes. One is via Highway 427 and the other via Avenue. He wants to study the

time it takes to drive to the airport using route and then compare the results. He

collected the following sample data, which is reported in minutes. Using the 0.10

significance level, is there a difference in the variation in the driving time using the

two routes?

Avenue Road Highway 427

52 59

67 60

56 61

45 51

70 56

54 63

64 57

65

Winter2011 3

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