1. ## Sampling

The head of a business school claims that the average MBA graduate is offered a starting salary of $55,000. The standard deviation of the offers is$4,600.

a) What is the probability that in a random sample of 38 MBA graduates, the mean starting salary is less than $53,000? I am saying that$\displaystyle P( \bar{X}< 53,000) = P\left(Z<\frac{53,000-55,000}{\frac{4,600}{\sqrt{38}}}\right)= \dots$b) What if only 16 students had been sampled? This is confusing, can I say$\displaystyle P(\bar{X}<53,000) = P\left(Z<\frac{53,000-55,000}{\frac{4,600}{\sqrt{16}}}\right)= \dots$?? as$\displaystyle \sigma$is known, can$\displaystyle Z$be used for$\displaystyle n=16$? 2. Originally Posted by Bushy The head of a business school claims that the average MBA graduate is offered a starting salary of$55,000. The standard deviation of the offers is $4,600. a) What is the probability that in a random sample of 38 MBA graduates, the mean starting salary is less than$53,000?

I am saying that

$\displaystyle P( \bar{X}< 53,000) = P\left(Z<\frac{53,000-55,000}{\frac{4,600}{\sqrt{38}}}\right)= \dots$

b) What if only 16 students had been sampled?

This is confusing, can I say

$\displaystyle P(\bar{X}<53,000) = P\left(Z<\frac{53,000-55,000}{\frac{4,600}{\sqrt{16}}}\right)= \dots$ ??

as $\displaystyle \sigma$ is known, can $\displaystyle Z$ be used for $\displaystyle n=16$ ?
Hint: You are given population mean and s.d. So what pdf does the sample mean follow?

3. Originally Posted by aman_cc
Hint: You are given population mean and s.d. So what pdf does the sample mean follow?

Will the mean be approximately normal? If so both my answers will be correct?

4. Originally Posted by Bushy
Will the mean be approximately normal? If so both my answers will be correct?
You have to make an underlying assumption of normality at least for the second as you have a small sample and you want to use the t-distribution.

For the first you may get away with relying on the CLT to justify normality, but I would still say I am assuming such (and for that matter also use the t-distribution).

CB