Question

A researcher wishes to report the average salary of mathematicians is strictly more than $50,000. She selects a sample of 100 math professors and finds the mean of the sample to be $51,260, with a standard deviation $5,230. Is there evidence to support the claim at α=0.05? Find the p-value

Answer 1

I am confused with finding the null and alternate hypothesis.

Answer 2

The null hypothesis is that the population avg salary is less than or equal to $50K
The estimate of the population standard deviation of $5,230 can lead us to an estimate of the standard error of the population mean of \[\frac{s}{\sqrt{n}} = \frac{$5,230}{\sqrt{100}}=\frac{$5,230}{10}=$523\]

Answer 3

So the estimate of the mean is $51,260. The threshold of $50K is $1,260 above the threshold which, when you divide by $523 gives a Z-score corresponding to a p value below 0.05.

Answer 4

Thank you.