Eighty-one random people were surveyed about the time it takes to commute to work in the morning. The standard deviation of the simple random sample is 2.3 minutes. The test statistic for the sample is 105.8. Find the critical values, using a significance level of 0.10, needed to test a claim that the standard deviation of all commute times is equal to 2.0 minutes. State the initial conclusion. Could anyone show me how to solve this?

For a 2-tail test (which this seems to be), with 80 dof and ɑ=0.1, the critical value from t-tables is 1.664.

If the T value is (2.3-2)/(2.3/√81)=1.17 as the test statistic, then 1.17<1.664, so the null hypothesis would be rejected, which means that the claim is incorrect and the standard deviation is not 2.0 minutes.

Initial conclusion may be that from the sample result, the population standard deviation is not 2.0 minutes, because the sample has SD=2.3 minutes.

The given test statistic of 105.8 doesn’t seem to tally with the other data. Perhaps it’s the mean commute time?

by Top Rated User (775k points)