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Practice 3: Test of a Single Variance

Module by: Susan Dean, Barbara Illowsky, Ph.D.. E-mail the authors

Summary: This module provides a practice on Chi-Square Distribution as a part of Elementary Statistics textbook.

Student Learning Outcomes

  • The student will conduct a test of a single variance.

Given

Suppose an airline claims that its flights are consistently on time with an average delay of at most 15 minutes. It claims that the average delay is so consistent that the variance is no more than 150 minutes. Doubting the consistency part of the claim, a disgruntled traveler calculates the delays for his next 25 flights. The average delay for those 25 flights is 22 minutes with a standard deviation of 15 minutes.

Sample Variance

Exercise 1

Is the traveler disputing the claim about the average or about the variance?

Exercise 2

A sample standard deviation of 15 minutes is the same as a sample variance of __________ minutes.

Solution

225

Exercise 3

Is this a right-tailed, left-tailed, or two-tailed test?

Hypothesis Test

Perform a hypothesis test on the consistency part of the claim.

Exercise 4

H o : H o : size 12{H rSub { size 8{O} } :μ rSub { size 8{W} } =μ rSub { size 8{ ital "NW"} } } {}

Exercise 5

H a : H a : size 12{H rSub { size 8{a} } :μ rSub { size 8{W} } <> μ rSub { size 8{ ital "NW"} } } {}

Exercise 6

Degrees of freedom =

Solution

24

Exercise 7

Chi2Chi2 size 12{ ital "Chi" rSup { size 8{2} } } {} test statistic =

Solution

36

Exercise 8

p-value =

Solution

0.0549

Exercise 9

Graph the situation. Label and scale the horizontal axis. Mark the mean and test statistic. Shade the p-value.

Blank graph with vertical and horizontal axes.

Exercise 10

Let α=0.05α=0.05 size 12{α=0 "." "05"} {}

Decision:

Conclusion (write out in a complete sentence):

Discussion Questions

Exercise 11

How did you know to test the variance instead of the mean?

Exercise 12

If an additional test were done on the claim of the average delay, which distribution would you use?

Exercise 13

If an additional test was done on the claim of the average delay, but 45 flights were surveyed, which distribution would you use?

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