Question

A sample of 75 concrete blocks had a mean mass of 38.3 kg with a standard deviation of 0.5 kg.

How many blocks must be sampled so that a 99% confidence interval will specify the mean mass to within ±0.1 kg? (Round up the final answer to the nearest integer.)

The number of blocks that must be sampled is

Answer 1

Solution :

Given that,

standard deviation =s =   =0.5

Margin of error = E = 0.1

At 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2 = 0.005

Z/2 = 2.58

sample size = n = [Z/2* / E] 2

n = ( 2.58*0.5 /0.1 )2

n =166.41

Sample size = n =166

if we take z value 3 decimal so answer is

n = ( 2.576*0.5 /0.1 )2

n =165.89

Sample size = n =166