A random sample of 20 purchases showed the amounts in the table (in $). The mean is $50.02 and the standard deviation is $19.84. 20.65 49.09 72.90 a) Construct a 90% confidence interval for the mean purchases of all customers, assuming that the assumptions and conditions for the confidence interval have been met. 3 29.35 33.46 b) How large is the margin of error? 81.87 20.48 35.27 c) How would the confidence interval change if you had assumed that the population standard deviation was known to be $20? 65.23 59.40 56.09 45.99 50.38 58.22 8 52.76 79.78 28.98 32.81 a) What is the confidence interval? (42.35 , 57.69 (Round to two decimal places as needed.) b) What is the margin of error? The margin of error is 7.67 (Round to two decimal places as needed.) c) What is the confidence interval using the given population standard deviation? Select the correct choice below and fill in the answer boxes within your choice. (Round to two decimal places as needed.) O A. The new confidence interval ( 42.66 , 57.37 ) is narrower than the interval from part a. O B. The new confidence interval ( ) is wider than the interval from part a