Question

Could you explain this to me? I'm really confused. I need to learn it step by step. Thank you so much! So this is the sample set

the s ample mean is 100 and the SD is 10 and the s ample size is 500.

Can you construct the 95 % confidence interval>

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 100
Population standard deviation =    = 500

Sample size n =10

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/  500 )

E= 0.8765
At 95% confidence interval estimate of the population mean
is,

- E < < + E

100-0.8765 <   < 100+ 0.8765

99.1235 <   < 100.8765

( 99.1235 , 100.8765 )