Question

Context: One of the longest and largest breeds of domesticated cats in the world is the Maine Coon.  A histogram of the weight of the cats of this breed reportedly approximately resembles a routine bell curve, and is distributed accordingly. The population standard deviation for the weight of this breed is approximately 2.5 pounds, according to one interpretation of veterinary statistics. Animal scientist and amateur statistician Angel Solstice collected an SRS of 64 Maine Coon cats and found their sample mean weight to be 20.425 pounds. If she wants to be 80% confident in her prediction of the true mean weight for all the cats of this breed, can she reasonably estimate the average weight for a Maine Coon at 20 pounds?  

a)  What is the corresponding software output using the CONFIDENCE function in Excel, expressed and rounded to six decimal places?

b) What is the lower bound for the 80% confidence interval about the population mean, rounded to four decimal places?

c) What is the upper bound for the 80% confidence interval about the population mean, rounded to four decimal places?

d) Based on these statistics, is a hypothesized value of 20 pounds a reasonable estimation of the population mean weight of these Maine Coon cats?

1. YES, highly reasonable as an estimate
2. YES, reasonable as an estimate
3. YES, marginally reasonable as an estimate
4. NO, marginally unreasonable as an estimate
5. NO, unreasonable as an estimate
6. NO, highly unreasonable as an estimate

Answer 1

x̅ = 20.425, σ = 2.5, n = 64

a) Using function in excel:

=CONFIDENCE.NORM(0.2, 2.5, 64) = 0.400485

b) Lower Bound = x̅ - E = 20.425 - 0.400485 = 20.0245

c) Upper Bound = x̅ + E = 20.425 + 0.400485 = 20.8255

d) NO, unreasonable as an estimate