Question

I did part 1 but need help with part 2

(Part 1) a food delivery service located at the edge of town and is responsible for serving a university. Testing different routes for getting from its location to campus, a driver finds that five trips using route A take an average of 5.9 minutes, with a standard deviation of 1.4 minutes; six trips using route B take an average of 4.2 minutes, with a standard deviation of 1.8 minutes. Assuming normal populations with equal standard deviations, and using the 0.10 level, is there a significant difference between the two routes?

(Part 2) Given the information given in part 1, and using a 0.05 level of significance, were we justified in assuming that the population standard deviations were equal?

Answer 1

1) H₀:

ol = 02

    H1:

ol #02

The test statistic F = $\frac{s_{1}^2}{s_{2}^2}$

                             

(1.82

                              = 0.6049

At 0.05 significance level, the critical values are

F_L= F(0.975,4,5) = 0.1068

F_R = F(0.025,4,5) = 7.3879

Since the test statistic value lies between the critical values(0.1068 < 0.6049 < 7.3879), so we should not reject the null hypothesis.

At 0.05 significance level, we can conclude that the population standard deviations are equal.