# How many business majors do we have to sample to estimate the mean salary to within \$1000 with 95% confidence? Question: Suppose we want to estimate the mean salary of all X-university students who graduated in Spring 2016 as business majors. In previous years, the standard deviation for these salaries was \$5000, i.e. $\sigma$ = 5000. How many business majors do we have to sample to estimate the mean salary to within \$1000 with 95% confidence? Approach: So the data is:$\sigma = 5000,\; \alpha=0.05,\; \overline{x} = 1000$Straight from the theory, I got that:$\overline{x}\pm Z_{\alpha/2}\left(\frac{\sigma}{\sqrt{n}}\right) = 1000\pm 1.96\left(\frac{5000}{\sqrt{n}}\right) $Is there a way to find$n$exactly or is the answers just: "we need to sample more than 30 students"? ## 1 Answer You know that $$\sigma =5000$$ $$ME=1000$$ The formula for finding the margin of error is given by $$\text{ME}=\frac{\sigma * Z}{\sqrt{n}}$$ You can solve algebraically for n now Thus, $$n=\left(\frac{\sigma * Z}{\text{ME}}\right)^2$$ Now, $$n=\left(\frac{1.96 * 5000}{1000}\right)^2$$ $$n=96.04$$ It might be safe to round this to 97. So in conclusion, 97 business majors would have to sampled to estimate the mean salary to within$1000 with 95% confidence

• I was a good idea to post your answer. Nice work. I was and I´m still confused. Therefore I to do some additional statistic work. – callculus Dec 2 '16 at 21:03