Question

The number of autos passing through a particular intersection between 4-5 PM on weekdays varies normally. If the population of numbers of autos passing through the intersection has a standard deviation σ = 48.4, and a sample of 100 weekdays has a mean of 652.4 cars passing through the intersection between 4-5 PM, test at the 5 % level of significance whether the mean number of cars passing through the intersection is different from 650. Make sure you set up the correct null and alternate hypotheses, indicate what kind of test is being performed, and perform the test.Use the critical value method of hypothesis testing. Do not worry about the p-value.

Answer 1

As we are testing here whether the mean number of cars passing through the intersection is different from 650, therefore the null and the alternative hypothesis here are given as:

The test statistic here is computed as:

As this is a two tailed test, we have from the standard normal tables: P(-1.96 < Z < 1.96) = 0.95

Therefore the rejection region here is Reject H0 if Z < -1.96 or Z > 1.96

As the given test statistic value is more than -1.96 that lies in the non rejection region, therefore the test is not significant and we cannot reject the null hypothesis here. Therefore we dont have sufficient evidence here that the mean is different from 650.