A random sample of 20 purchases showed the amounts in the table (in $). 20.20 21.74 62.41 82.16 44.39 45.32 66.55 46.67 27.15 51.24 85.64 31.84 71.85 53.02 33.74 86.93 14.81 54.32 77.23 59.17 The mean is $51.82 and the standard deviation is $22.32. a.) what is the standard error of the mean? (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 fill in any blanks within your choice? a.) the standard error would increase. The new standard error would be ___ times the old? b.) The standard error would decrease. The new standard error would be the old standard error divided by ___? c.) The standard error would not change