Question

An airline claims that its flights are consistently on time with an average delay of at most 11 minutes. It claims that the average delay is so consistent that the variance is no more than 92 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 23 minutes with a standard deviation of 17 minutes. Assume α = 0.05. Is the traveler disputing the claim about the average or about the variance? A sample standard deviation of 17 minutes is the same as a sample variance of minutes. Determine the type of test: State the null and the alternative hypotheses: H 0 : H a : Identify the claim: Identify the distribution to use for the test: . The degrees of freedom: . Calculate the χ 2 statistic: . [Round your answer to 3 decimal places.] Forgot the formula? Critical Value Method Calculate the critical value: . [Round your answer to 3 decimal places.] Decision: Reason for decision: p-Value Method Calculate the p-Value: . [Round your answer to 4 decimal places.] Decision: Reason for decision: Conclusion of the hypothesis test: There is evidence at α = 0.05 level of significance to the claim that the standard deviation of delays is no more than 10 minutes.

Answer 1

since the airline is claiming about variance,so the traveller disputing the claim about variance.

sample variance,s^2=17*17=289

null hypothesisdelay:variance is no more than 92 minutes(claim)

alternate hypothesis:delay variance is greater than 92 minutes

there is enough evidence to reject the airline claim thatdelay variance is no more than 92 at 0.05 level.

p value=0.00 (chi square statistic=75.391,DF=n-1=25-1=24)

since p value less than alpha value,reject Ho

which is same decision as critical value method.