Question

You measure 48 textbooks' weights, and find they have a mean weight of 64 ounces. Assume the population standard deviation is 12.3 ounces. Based on this, construct a 90% 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 = = 64

Population standard deviation = = 12.3

Sample size = n = 48

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z/2 = Z0.05 = 1.645

Margin of error = E = Z/2* ( /n)

= 1.645 * (12.3 / 48 )

= 2.92

At 90% confidence interval estimate of the population mean is,

- E < < + E

64 - 2.92 < < 64 + 2.92

61.08 < < 66.92