Question

1. 1) a) A public bus company official claims that the mean waiting time for bus number 14 during peak hours is less than 10 minutes. Karen took bus number 14 during peak hours on 18 different occasions. Her mean waiting time was 8.2 minutes with a standard deviation of 1.6 minutes. At the 0.01 significance level, test the claim that the mean waiting time is less than 10 minutes. Use the traditional (rejection region) method of testing.

   b) Use the sample statistics above to create a 95% confidence interval for the mean waiting time for bus number 14 during peak hours. After writing the confidence interval, explain whether or not (and reason!) the results match the conclusion of your hypothesis test above. (Hint: Do not just write a confidence interval statement.)

Answer 1

a)

H0: >= 10

Ha: < 10

Test statistics

t = ( - ) / ( S / sqrt(n) )

= (8.2 - 10) / (1.6 / sqrt(18) )

= -4.77

Critical value at 0.01 level with 17 df = -2.898

Rejection region = reject H0 if test statistics t < -2.898

Since test statistics falls in rejection region, Reject H0.

b)

t critical value at 0.05 level with 17 df = 2.110

95% confidence interval for is

- t * S / sqrt(n) < < + t * S / sqrt(n)

8.2 - 2.11 * 1.6 / sqrt(18) < < 8.2 + 2.11 * 1.6 / sqrt(18)

7.40 < < 9.00

95% CI is (7.40 , 9.00)

Since claimed mean 10 is not contained in confidence interval (And all values in confidence interval )

are less than 10, we have sufficient evidence to support the claim.

The result match with conclusion drawn in part a)