The Chi-Square Distribution: Practice 3 1.5 2008/06/22 21:08:19 GMT-5 2008/08/15 13:36:39.419 GMT-5 Barbara Illowsky illowskybarbara@deanza.edu Susan Dean deansusan@deanza.edu Connexions cnx@cnx.org elementary statistics This module provides a practice on Chi-Square Distribution as a part of Elementary Statistics textbook.

Student Learning Outcomes The student will explore the properties of data with 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? A sample standard deviation of 15 minutes is the same as a sample variance of __________ minutes. 225 Is this a right-tailed, left-tailed, or two-tailed test?

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"} } } {} H a : size 12{H rSub { size 8{a} } :μ rSub { size 8{W} } <> μ rSub { size 8{ ital "NW"} } } {} Degrees of freedom = 24 Chi2 size 12{ ital "Chi" rSup { size 8{2} } } {} test statistic = 36 p-value = 0.0549 Graph the situation. Label and scale the horizontal axis. Mark the mean and test statistic. Shade the p-value. Let α=0.05 size 12{α=0 "." "05"} {} Decision: Conclusion (write out in a complete sentence):

Discussion Questions How did you know to test the variance instead of the mean? If an additional test were done on the claim of the average delay, which distribution would you use? If an additional test was done on the claim of the average delay, but 45 flights were surveyed, which distribution would you use?