Historically, the average waiting time spent on hold when phoning customer service for a particular bank was one and a half minutes. To determine whether the average time people were waiting had improved since they changed the customer service staff manager, the bank undertook a random sample of the waiting time recorded by 15 customers. The results are in the Y column (in seconds) of the data file P14.12.xls which can be found in a folder under the CML Quizzes tab. Assume that the test is performed at the 10% level of significance and that the distribution of waiting times is approximately normally distributed.
1. State the direction of the alternative hypothesis used to test whether average waiting time had improved. Type gt (greater than), ge (greater than or equal to), lt (less than), le (less than or equal to) or ne (not equal to) as appropriate in the box.
2. Calculate the test statistic correct to three decimal places (hint: use Descriptive Statistics to calculated the standard deviation and sample mean).
3. By referring to the appropriate Z or t-table, which of the following four given numbers is most likely to be the actual p-value for the test? Namely, 0.0900, 0.1800, 0.4207 or 0.4222. Enter your chosen number as your answer, using all four decimal places.
4. Is the null hypothesis rejected for this test? Type yes or no.
5. Regardless of your answer for 4, if the null hypothesis was rejected, could we conclude that the average waiting time is more than 90 seconds at the 10% level of significance? Type yes or no.