A restaurant owner believed that customer spending was below normal at tables manned by one of the waiters. The owner sampled 36 checks from the waiter's tables and got the following amounts (rounded to the nearest dollar):
|
47
|
46
|
56
|
70
|
52
|
58
|
48
|
57
|
49
|
61
|
52
|
40
|
|
60
|
22
|
74
|
59
|
60
|
30
|
61
|
44
|
62
|
41
|
53
|
57
|
|
50
|
52
|
57
|
59
|
69
|
51
|
58
|
56
|
44
|
36
|
47
|
51
|
Note that Σx = 1889 and Σx2 = 103,027.
(a) Find a 95% confidence interval for the mean amount of money µ spent at the waiter's tables.
(b) Does it appear that the mean amount spent at the waiter's tables is smaller than the restaurant average of $55?