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 <
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
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