Question

1.)

A person can take either of two routes to work, through Matteson or Richton Park. Both take on average 35 minutes, and travel times are Normally distributed. But are the variances of the travel times different? A random sample with n = 8 using the Matteson route, and another random sample with n = 6 using the Richton Park route, showed a variance of 40 (units: square minutes) and 30 respectively. To test whether the variances are different, the following test of hypothesis is to be carried out: HO: 07 = 0 H1: 0+ To test this at 5% level of significance, what is the critical value for the test statistic? (Give two decimal places)

2.)

Answer 1

1) Numerator df = 8 - 1 = 7

Denominator df = 6 - 1 = 5

For 7 numerator df, 5 denominator df and 5% significance level:

Critical value = 4.88

2) Standard deviation = $\sqrt{Variance} = \sqrt{20}$ = 4.47