Question

You measure 22 textbooks' weights, and find they have a mean weight of 44 grams. Assume the population standard deviation is 12.5 grams. Based on this, construct a 95% confidence interval for the true population mean textbook weight. Assume n is sufficiently large so the normal test can be used.

Give your answers as decimals, to two places

______ < μ < _____

Answer 1

Solution :

Given that,

Point estimate = sample mean =     = 44

Population standard deviation =    =12.5

Sample size n =22

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* (12.5 / 22 )

= 5.22
At 95% confidence interval estimate of the population mean
is,

- E < < + E

44 - 5.22 <   < 44+ 5.22

38.78 <   <49.22