Question

You measure 21 textbooks' weights, and find they have a mean weight of 46 ounces. Assume the population standard deviation is 8.1 ounces. Based on this, construct a 95% confidence interval for the true population mean textbook weight.

Give your answers as decimals, to two places

< μ <

Answer 1

Solution :

Given that,

sample mean = = 46

Population standard deviation =    = 8.1

Sample size = n =21

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* (8.1 /  21 )

= 3.46
At 95% confidence interval estimate of the population mean
is,

- E < < + E

46-3.46 , 46+3.46

(42.54 < μ < 49.46)