Question

Historically, the average time a customer takes with a teller at a particular bank was 130 seconds. To determine whether the average time with the teller had changed since they changed the staff manager, the bank undertook a random sample of the waiting time (in seconds) recorded by 15 customers. The results are below: Y X1 X2 28 12.6 134 43 11.4 126 45 11.5 143 49 11.1 152 57 10.4 143 68 9.6 147 74 9.8 128 81 8.4 119 82 8.8 130 86 8.9 135 101 8.1 141 112 7.6 123 114 7.8 121 119 7.4 129 124 6.4 135 Assume that the test is performed at the 5% 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 changed. 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, 0.1650, 0.4292, 0.0708, or 0.7213. 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 time is not 130 seconds at the 5% level of significance? Type yes or no.

          Historically, the average time a customer takes with a teller at
a particular bank was 130 seconds. To determine whether the average
time with the teller had changed since they changed the staff
manager, the bank undertook a random sample of the waiting time (in
seconds) recorded by 15 customers. The results are below:
Y    X1    X2
28    12.6    134
43    11.4    126
45    11.5    143
49    11.1    152
57    10.4    143
68    9.6    147
74    9.8    128
81    8.4    119
82    8.8    130
86    8.9    135
101    8.1    141
112    7.6    123
114    7.8    121
119    7.4    129
124    6.4    135
Assume that the test is performed at the 5% 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 changed. 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, 0.1650, 0.4292, 0.0708,
or 0.7213. 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 time is not 130
seconds at the 5% level of significance? Type yes or no.

Added by David W.

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