Question

Check My Work eBook How large a sample should be selected to provide a 95% confidence interval with a margin of error of 8? Assume that the population standard deviation is 10, Round your answer to next whole number. Check My Work ๛ Icon Key Exercise 08.23 Algorithmic Question 12 of 20

Answer 1

Solution:

Given ,

$\sigma$= 10 ..Population SD

E= 8 Margin of error

c= 95% =0.95 ...confidence level

Find sample size required.

c = 0.95

$\therefore$$\alpha$ = 1- c = 1- 0.95 = 0.05

$\therefore$  $\alpha$/2 = 0.05 $\slash$ 2 = 0.025 and 1- $\alpha$ /2 = 0.975

Search the probability 0.975 in the Z table and see corresponding z value

$\therefore$$Z_{\alpha/2}$ = 1.96 for the 95% Confidence level.

Now, sample size (n) is given by,

$n = [\frac{Z_{\alpha/2}*\sigma}{E}]^{2}$

= {(1.96* 10 )/ 8 }^2

= 6.0025

=7

So , answer is 7