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.

DERIVE a formula to create these upper bounds. i.e a formula such that when applied to the random samples {X1, X2, · · · , Xn} , the values obtained on 99% of the samples will be really greater than the true average mass of the birds. Note that sample size n can be any positive integer greater than 2.

Answer 1

Solution:-

Given that

Assume that body masses of Goldfinch birds follow a normal distribution, with standard deviation equal to 0.05 oz.

In particular, she would like to create a 99% upper confidence bound, which is described below, for the average body mass of Goldfinch birds.

Dervive a formula to create these upper bounds. i.e a formula such that when applied to the random samples {X1, X2, .... Xn}, the values obtained on 99% of the samples will be really greater than the true average mass of the birds. Note that sample size n can be any positive integer greater than 2.

Given that population standard deviation

C = 99%

level of significance = 1 - 0.99

= 0.01

Z critical value at = 2.576

margin of error

  

  

99% confidence interval = sample mean margin of error

Therefore Upper bound of CI

Where n is sample size n greater than 2

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