Question

An admissions director wants to estimate the mean age of all students enrolled at a college. The estimate must be within 1.3 years of the population mean. Assume the population of ages is normally distributed.​(a) Determine the minimum sample size required to construct a 90​% confidence interval for the population mean. Assume the population standard deviation is 1.5 years.

Answer 1

Answer: 4

Step-by-step explanation:

For given Population standard deviation$(\sigma)$ , the formula to sample size is given by :-

$n=(\dfrac{\sigma\cdot z*}{E})^2$

, where z* = Two-tailed critical value.

E = Margin of error.

Given : $\sigma=1.5$ years

We know that , Critical value for 90​% confidence interval : z* = 1.645

Margin of error : E=1.3 years

Then, the minimum sample size required to construct a 90​% confidence interval  for the population mean will be :-

$n=(\dfrac{1.5\cdot 1.645}{1.3})^2\\\\=(1.89807692308)^2\\\\=3.60269600593\approx4$ [Rounded to the nearest whole number.]

Hence, the minimum sample size required = 4