Question

Sarah is doing research on the average age of first-year resident physicians. She wants her estimate to be accurate to within 1 year. From past studies, she knows the population standard deviation is 8.265. How many first-year residents must she survey to be 95% confident?

Answer 1

Answer: The number of first-year residents she must survey to be 95% confident= 263

Step-by-step explanation:

When population standard deviation ($\sigma$)  is known and margin of error(E) is given, then the minimum sample size (n) is given by :-

$n=(\dfrac{z^*\sigma}{E})^2$, z* = Two-tailed critical value for the given confidence interval.

For 95% confidence level , z* = 1.96

As, $\sigma$ = 8.265, E = 1

So, $n= (\dfrac{1.96\times8.265}{1})^2 =(16.1994)^2\\\\= 262.42056036\approx263\ \ \ [\text{Rounded to the next integer}]$

Hence, the number of first-year residents she must survey to be 95% confident= 263