Question

Can you explain step by step for me? "Dumb it down"? I need a lot of help with this question. Thank you so much!

This is the sample set. The s ample mean is 100 and the SD is 10 and the s ample size is 400.

Construct the 95% confidence interval?

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 100

Population standard deviation =    = 10

Sample size n =400

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

Margin of error = E = Z/2 * ( /n)

= 1.96 * ( 10 /  400 )

E= 0.98
At 95% confidence interval estimate of the population mean
is,

- E < < + E

100- 0.98<   <100 + 0.98

99.02 <   < 100.98

( 99.02 , 100.98 )