Question

The city of Chicago has for many years reported that the average distance from home to

work for its employed residents is 12.60 miles. A researcher believes that the average is now shorter, and

collects data on a random sample of 17 employed Chicagoans. In that sample, the mean distance to work

was 10.25 miles, with standard deviation 3.62.

Using significance level .05, test these claims. Show all steps covered in class, including any notation used

for the setup of the problem.

Answer 1

Here we want to test miles.

Given that the sample size n=17, mean distance .

The test statistic used for this test is, which is distributed as a standard normal variable.

The value of the test statistic under the null hypothesis is ,

That is we reject H0 in favour of alternative hypothesis. That is we rect H0 when the calculated value is less than .Where is the value obtained from the standard normal table corresponding to 0.95 probability. That is (one sided test).

Since -2.6766 is less than -1.64 we reject the null hypothesis. Hence the average distance from home to

work for its employed residents is less than 12.60 miles.