<< Chapter < Page Chapter >> Page >
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

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

Got questions? Get instant answers now!

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

225

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

Hypothesis test

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

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

36

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

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

Decision:

Conclusion (write out in a complete sentence):

Got questions? Get instant answers now!

Discussion questions

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Collaborative statistics. OpenStax CNX. Jul 03, 2012 Download for free at http://cnx.org/content/col10522/1.40
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Collaborative statistics' conversation and receive update notifications?

Ask