Fancy pets are big business, so a young entrepreneur (age 12) decided to breed golden hamsters, a type well known to pet stores and collectors. (Oddly enough, nearly all the golden hamsters in captivity are descendants of one litter found in Syria in 1930.) Of 47 recent litters, there were an average of 7.27 baby hamsters with a standard deviation of 2.5 hamsters per litter.

a) Find and interpret a 90% confidence interval for the mean litter size.

b) How much smaller or larger would the margin of error be for a 99% confidence interval? Explain.

c) Based on these statistics, how many litters would we need to estimate the mean litter size to within one baby hamster with 95% confidence?