Question

Assume that population means are to be estrimated from the samples described. Use the sample results to approximate the margin of error and 95% confidence interval. Sample Size= 144. Sample mean = 81. Sample standard deviation=6.

Answer 1

Solution:

   Given :

Sample Size = n = 144

Sample mean =

Sample Standard Deviation = s = 6

Confidence level = c = 95%

We have to find Margin of Error and confidence interval.

Margin of Error =

Since sample size n = 144 is large ( > 30 ) . thus we can use Approximate Normal distribution.

Population standard deviation is unknown , hence we use sample estimate of standard deviation s.

we have to find z value for 95% confidence level.

Find area = ( 1 + c) / 2 = ( 1 + 0.95 ) /2 = 1.95 / 2 = 0.9750

Look in z table for area = 0.9750 and find corresponding z value.

Area 0.9750 corresponds to 1.9 and 0.06

Thus z =1.96

Thus Margin of Error =

Thus Margin of Error =

95% confidence interval is :