Amie Jackson,a manager at Sigma travel services,makes every effort to ensure that customers attempting to make online reservations do not have to wait too long to complete the reservation process.The travel website is open for reservations 24 hours a day,and Amie regularly checks the website for the waiting time to maintain consistency in service.She uses the following independently drawn samples of wait time during two peak hours,morning 8a.m.to 10 a.m.and evening 7p.m.to 9p.m. ,for the analysis.Assume that wait times are normally distributed. At the 10% significance level,which of the following is the correct conclusion? A) Do not reject H₀.We cannot conclude that the variance of wait time during morning peak hours differs from that during the evening peak hours. B) Reject H₀.We conclude that the variance of wait time during morning peak hours differs from that during the evening peak hours. C) Do not reject H₀.We conclude that the variance of wait time during morning peak hours differs from that during the evening peak hours. D) Reject H₀.We cannot conclude that the variance of wait time during morning peak hours differs from that during the evening peak hours.

Question

Quizplus · Accepted Answer

We need to perform a two-sample F-test for the equality of variance. The null hypothesis is that the variance of wait time during morning peak hours is equal to that during the evening peak hours. The alternative hypothesis is that the variance of wait time during morning peak hours differs from that during the evening peak hours. We can use the F-test formula to calculate the test statistic:

F = s1^2 / s2^2

where s1^2 is the sample variance of morning peak hours and s2^2 is the sample variance of evening peak hours. The degrees of freedom for the two samples are n1 - 1 and n2 - 1, respectively.

Using the given data, we get:

s1^2 = 62.8, s2^2 = 48.4, n1 = 30, n2 = 30

Plugging these values into the formula, we get:

F = 62.8 / 48.4 = 1.2971

The critical F-value for a 10% significance level with 29 degrees of freedom in the numerator and 29 degrees of freedom in the denominator is 1.521. Since our calculated F-value is less than the critical F-value, we fail to reject the null hypothesis. Therefore, we conclude that the variance of wait time during morning peak hours does not differ significantly from that during the evening peak hours.

Amie Jackson,a Manager at Sigma Travel Services,makes Every Effort to Ensure