Question

A 95% confidence interval for the mean of a population is to be constructed and must be accurate to within 0.3 unit. A preliminary sample standard deviation is 3.8. The smallest sample size n that provides the desired accuracy is

Answer 1

Answer:

Sample size should be atleast 617

Step-by-step explanation:

given that a 95% confidence interval for the mean of a population is to be constructed and must be accurate to within 0.3 unit.

i.e. margin of error <0.3

Std devition sample = 3.8

For 95% assuming sample size large we can use z critical value

Z critical = 1.96

we have

$1.96 * std error <0.3\\1.96(\frac{3.8}{\sqrt{n} } )<0.3\\\sqrt{n} >24.83\\n>616.3634$

Sample size should be atleast 617 to get an accurate margin of error 0.3