Question

A 95% confidence interval for a population mean was reported to be 150 to 160 . If standard deviation = 17, what sample size was used in this study? (Round your answer to next whole number.)

Answer 1

Solution:

Given that,

Confidence interval = ( 150, 160)

The sample mean is ,

$\bar{x}$ = ( Lower confidence bound+ Upper confidence bound) / 2

= (150 + 160) / 2

= 155

The margin of error is,

E = Upper confidence bound- $\bar{x}$

= 160 - 155

= 5

At 95% confidence level the t is ,

$\alpha$ = 1 - 95% = 1 - 0.95 = 0.05

$\alpha$ / 2 = 0.05 / 2 = 0.025

Z_$\alpha$/2 = Z_0.025 = 1.96

sample size = n = (Z_$\alpha$/2* $\sigma$ / E) ²

n = (1.96 * 17/ 5)²

n = 44.41

n = 45

Sample size = 45