Posted by Amy on .
A study in Orlando, Florida claimed that the mean commute time for all employees working at Disney exceeds 40 minutes. This figure is higher than what was assumed in the past. The plan is to test this claim at a level of significance = 0.05 and a sample size = 100 commuters. For this sample size, it was found the sample mean is 43.5 minutes. Based on previous studies, assume the standard deviation is known to be o = 8 minutes. Conduct a hypothesis test using a rejection region and draw a conclusion.
Try a one-sample z-test.
Ho: µ = 40 -->null hypothesis
Ha: µ > 40 -->alternate hypothesis
z = (sample mean - population mean)/(standard deviation divided by the square root of the sample size)
With your data:
z = (43.5 - 40)/(8/√100) = ?
Finish the calculation.
Check a z-table at level 0.05 for a one-tailed test.
If the z-test statistic exceeds that value from the z-table, reject the null and conclude µ > 40. If the z-test statistic does not exceed the that value from the z-table, do not reject the null (you cannot conclude a difference).
I hope this will help get you started.