Question

The director of the IRS has been flooded with complaints that people must wait more than 35 minutes before seeing an IRS representative. To determine the validity of these complaints, the IRS randomly selects 400 people entering IRS offices across the country and records the times which they must wait before seeing an IRS representative. The average waiting time for the sample is 50 minutes with a standard deviation of 23 minutes. Is there overwhelming evidence to support the claim that the wait time to see an IRS representative is more than 35 minutes at a 0.025 significance level?

Step 1 of 3 :

Find the value of the test statistic. Round your answer to three decimal places, if necessary.

Answer 1

The null and alternative hypothesis for the test are:

Null Hypothesis, , i.e., the true average waiting time for seeing an IRS representative is not different than 35 minutes or Not greater than 35 minutes.

Alternative Hypothesis, , i.e., the true average waiting time for seeing an IRS representative is Greater than 35 minutes.

We have to test this hypothesis at given given significance level of

A random sample of people and the waiting time for people in this sample has sample mean of and the sample standard deviation of .

Test-statistic:

The formula for calculating the test-statistic is:

So, the test-statistic is calculated as

Critical value: It is used to make a decision, whether to Reject Or Not to reject null hypothesis.

Since, the significance level is .

So, the critical value is

Decision: test-statistic, and the critical value,

Since,

So, at given significance level, the sample data provides sufficient evidence to reject null hypothesis. Hence, we conclude that, based on sample data we have enough evidence to believe that the alternative hypothesis is True, i.e., , that is the true average waiting time before seeing an IRS representative is greater than 35 minutes.