Question

You measure 44 textbooks' weights, and find they have a mean weight of 55 ounces. Assume the population standard deviation is 4.1 ounces. Based on this, construct a 95% confidence interval for the true population mean textbook weight. Give your answers as decimals, to two places

< μμ <

Answer 1

Solution :

Given that,

Point estimate = sample mean =     = 55

Population standard deviation =    =4.1

Sample size n =44

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 * ( 4.1 / 44)

= 1.21
At 95% confidence interval estimate of the population mean
is,

- E < < + E

55- 1.21 <   < 55 + 1.21

53.79 <   < 56.21