Question

A community survey sampled 1923 people in Colorado and asked them how long it took them to commute to work each day. The sample mean one-way commute time was 25.3 minutes with a standard deviation of 13 minutes. A transportation engineer claims that the mean commute time differs from 25 minutes. Do the data provide convincing evidence that the engineer's claim is true? Use the α=0.01 level of significance and the P-value method with the Critical Values for the Student's t Distribution Table.

(a) State the appropriate null and alternate hypotheses.

H0:

H1:

This hypothesis test is a.

(b) Compute the value of the test statistic. Round the answer to at least three decimal places.

(c)Determine whether to reject H0.

Answer 1

Solution :

This is two tailed test .

The null and alternative hypothesis is ,

H0 :   = 25

Ha : 25

Test statistic (t)

= ( - ) / s / n

= (25.3 - 25) / 13 / 1923

Test statistic = 1.012

P-value = 0.3117

= 0.01

P-value >

Fail to reject the null hypothesis