Historically, the average waiting time spent in a queue on Friday afternoon at a bank's city branch was 10 minutes. To determine whether their new multi-queuing system constitutes an improvement, a random sample of 15 customers was taken and their waiting time recorded. The results are in the X1 column below the questions. Assume the distribution of waiting times is normally distributed.

1. State the direction of the alternative hypothesis used to test whether there is an improvement in average waiting time. Greater than, greater than or equal to, less than, less than or equal to or not equal to?

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 actualp-value for the test? Namely, 0.0814, 0.0515, 0.4292 or 0.4306. Enter your chosen number as your answer, using all four decimal places.

4. Is the null hypothesis rejected for this test if a 5% level of significance is used? yes or no.

5. Regardless of your answer for 4, if the null hypothesis was rejected, can we conclude that the average waiting time has improved with the new queuing system? yes or no.

Y X1

28 12.6

43 11.4

45 11.5

49 11.1

57 10.4

68 9.6

74 9.8

81 8.4

82 8.8

86 8.9

101 8.1

112 7.6

114 7.8

119 7.4

124 6.4