Question

Suppose you do an analysis of the starting salaries of 100 recent Lehman graduates. You find that the average starting salary is $60,000 with a standard deviation of $5,000.

a. Find the 90% critical values.
b. Find the 95% critical values.

Answer 1

a) (59180,60820)

b) (59020,60980)

Explanation:

We are given the following information in the question:

Mean, μ = $60,000

Standard Deviation, σ = $5,000

Sample size, n = 100

a) 90% critical values

`\mu \pm z_(critical)(\sigma)/(√(n))`

Putting the values, we get,

`z_(critical)\text{ at}~\alpha_(0.10) = 1.64`

`60000 \pm 1.64((5000)/(√(100)) ) = 60000 \pm 820 = (59180,60820)`

b) 95% critical values

`\mu \pm z_(critical)(\sigma)/(√(n))`

Putting the values, we get,

`z_(critical)\text{ at}~\alpha_(0.05) = 1.96`

`60000 \pm 1.96((5000)/(√(100)) ) = 60000 \pm 980= (59020,60980)`