Question

Assume that body masses of Goldfinch birds follow a normal distribution, with standard deviation equal to 0.05 oz. Imagine that you are asked to help an ornithologist who would like to make some inference about the average body mass of Goldfinch birds. In particular, she would like to create a 99% upper confidence bound, which is described below, for the average body mass of Goldfinch birds.

Let 0.40, 0.45, 0.49, 0.52 ,in unit of oz, be 4 measurements of body mass from 4 randomly selected Goldfinch birds. Based on the given sample data, compute a 99% upper confidence bound and state what your inference/conclusion is.

Answer 1

solution:

the given information as follows:

sample data is 0.40, 0.45, 0.49, 0.52

sample mean =

population standard deviation = oz

confidence level = 99% = 0.99

= 1-0.99 = 0.01

critical value of z =

margin of error =

upper bound of the intrval = = 0.465 + 0.064 = 0.529

with 99% confidence it can be said that the mean body mass of goldfinch birds are less than 0.529 oz.