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?  

Question:What is the level of significance, or , that corresponds to an 80% confidence level, expressed as a percentage?

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis: μ = 20
Alternative Hypothesis: μ ≠ 20

Rejection Region
This is two tailed test, for α = 0.2
Critical value of z are -1.28 and 1.28.
Hence reject H0 if z < -1.28 or z > 1.28

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (20.425 - 20)/(2.5/sqrt(64))
z = 1.36

P-value Approach
P-value = 0.1738
As P-value < 0.2, reject the null hypothesis.

Alpha = 1-0.80 = 0.2