A random sample of 20 purchases showed the amounts in the table (in S). The mean is $50.34 and the standard deviation is S25.29. a) What is the standard error of the mean? b) How would the standard error change if the sample size had been 5 instead of 20? (Assume that the sample standard deviation didn't change.) 3.74 22.60 5.92 44.94 45.47 45.62 66.64 47.64 49.41 69.71 70.45 30.90 85.54 31.74 34.49 88.08 88.41 57.15 38.88 79.42 a) The standard error of the mean is (Round to two decimal places as needed.) b) How would the standard error change if the sample size was 5 instead of 20 with the same sample standard deviation? Select the correct choice below and fll in any answer boxes within your choice. OA. The standard error would increase. The new standard error would betimes the old. O B. The standard error would decrease. The new standard error would be the old standard error divided by O C. The standard error would not change