iQ7 In some literature a coach company claims that the media

iQ7

In some literature, a coach company claims that the median journey time for its services between Bristol and Aberdeen is 13 hours.

A couple of regular passengers are interested in whether or not this claim is correct. To test this they timed how long the journey took on some of the occasions they made the trip. For a total of 24 trips between Bristol and Aberdeen, they found that 15 of the trips were shorter than 13 hours, 7 of the trips took longer than 13 hours and 2 of the trips took exactly 13 hours.

Suppose a sign test is carried out to test the hypothesis that the median journey time is 13 hours. Select the TWO statements which are TRUE.

A) The test statistic is 24.

B) The sample size that should be used in the test is 24.

C) The test statistic is 7.

D) The test statistic is 6.

E) The test statistic is 5.

F) The test statistic is 22.

G) The test statistic is 15.

H) The sample size that should be used in the test is 2.

I) The sample size that should be used in the test is 22.

Solution

In the case while statement B is evidently correct as the sample size is 24 i.e. the number of trips taken to confirm the claim,

However, all other options are with respect to the test statistic. the test statistic is quite clearly the sample median which is 13, also signifies the claim to be tested . Hence, the test statistic is 13.