Question

You measure 43 textbooks' weights, and find they have a mean weight of 37 ounces. Assume the population standard deviation is 11.5 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 = = 37

Population standard deviation =    = 11.5

Sample size = n = 43

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z_{0.05 = 1.645}

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

= 1.645 * ( 11.5 /  43 )

= 2.88

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

- E < < + E

37 - 2.88 <   < 37 + 2.88

( 34.12 <   < 39.88 )