Question

Suppose that a simple random sample is taken from a normal population having a standard deviation of

15

for the purpose of obtaining a

95​%

confidence interval for the mean of the population.

a. If the sample size is

44​,

obtain the margin of error.

b. Repeat part​ (a) for a sample size of

25

Answer 1

Here we take the simple random sample from a normal population having a standard deviation of 15 for the purpose of obtaining a 95​% confidence interval for the mean of the population.

a) Here sample size n = 44

Formula of margin of error ( E ) is as follows:

........( 1 )

For 95% confidence level the critical Z value ( ) is 1.96

= 15 and n = 44

Plug these values in equation ( 1 ), we h=get :

1.96 15 4.4322

b) for n = 25