Question

You measure 40 textbooks' weights, and find they have a mean weight of 73 ounces. Assume the population standard deviation is 4.7 ounces. Based on this, construct a 95% confidence interval for the true population mean textbook weight.

Give your answers as decimals, to two places

I am 95% confident that the mean weight of textbooks is between  and  ounces.

Answer 1

Solution :

Given that,

Point estimate = sample mean =     = 73

Population standard deviation =     = 4.7

Sample size n =40

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* ( 4.7/ 40 )

E= 1.46
At 95% confidence interval estimate of the population mean
is,

- E <   < + E

73-1.46 <   < 73+1.46

71.54 <   < 74.46

( 71.54 and  74.46 )