Question

) A major airline is concerned that the waiting time for customers at its ticket counter may be exceeding its target average of 190 seconds. To test this, the company has selected a random sample of 100 customers and times them from when the customer first arrives at the checkout line until he or she is at the counter being served by the ticket agent. The mean time for this sample was 202 seconds with a standard deviation of 28 seconds. Given this information and the desire to conduct the test using an alpha level of 0.02, which of the following statements is true?
A) The chance of a Type II error is 1 - 0.02 = 0.98.
B) The test to be conducted will be structured as a two-tailed test.
C) The test statistic will be approximately t = 4.286, so the null hypothesis should be rejected.
D) The sample data indicate that the difference between the sample mean and the hypothesized population mean should be attributed only to sampling error.

Answer 1

Solution

Option C Answer

Justification

Type II error is that of accepting the null hypothesis when it is not true and Type I error is that of rejecting the null hypothesis when it is true. Clearly, one is not the compliment of the other. Noting that 0.02 given is also the alpha level which is the chance of commiting Type I error.

So, A is not true.

Given, ‘A major airline is concerned that the waiting time for customers at its ticket counter may be exceeding its target average of 190 seconds.’ => the Alternative hypothesis is average > 190. This is clearly a one-sided test. So, (B) is not true.

To check the validity of (C), we need to do the following calculations:

t = = (√100)(202 – 190)/28

= 4.2857.

Critical value = upper 2% point of t₉₉ = 2.3646.

Since t > Critical value, null hypothesis should be rejected.

So, (C) is true.

If (C) is true, (D) cannot be true because (D) actually implies null hypothesis is accepted.

Answer

DONE