Question

You measure 50 textbooks' weights, and find they have a mean weight of 77 ounces. Assume the population standard deviation is 12.8 ounces. Based on this, construct a 90% confidence interval for the true population mean textbook weight.

Give your answers as decimals, to two places

< μ <

Answer 1

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± Z*σ/sqrt(n)

From given data, we have

Xbar = 77

σ = 12.8

n = 50

Confidence level = 90%

Critical Z value = 1.6449

(by using z-table)

Confidence interval = Xbar ± Z*σ/sqrt(n)

Confidence interval = 77 ± 1.6449*12.8/sqrt(50)

Confidence interval = 77 ± 2.9775

Lower limit = 77 - 2.9775 = 74.02

Upper limit = 77 + 2.9775 = 79.98

Confidence interval = (74.02, 79.98)

74.02 < µ < 79.98