A random sample of 20 purchases showed the amounts in the table(in $). The mean is $49.78 and the standard deviation is $21.76.

40.54

46.49

57.08

21.13

28.45

37.57

41.62

70.26

38.19

41.72

31.07

78.85

43.51

71.89

79.47

82.87

32.87

89.74

46.21

15.97

a) Construct a 98% confidence interval for the mean purchases of allcustomers, assuming that the assumptions and conditions for the confidence interval have been met.

b) How large is the margin oferror?

c) How would the confidence interval change if you had assumed that the standard deviation was known to be $22?

a) What is the confidenceinterval?

(Round to two decimal places asneeded.)

b) What is the margin oferror?

The margin of error is ______

(Round to two decimal places asneeded.)

c) What is the confidence interval using the given population standarddeviation? Select the correct choice below and fill in the answer boxes within your choice.

(Round to two decimal places asneeded.)

A.

The new confidence interval ( ),( ) is narrower than the interval from part a.

B.

The new confidence interval ( ), ( )is wider than the interval from part a.