Give your answers as decimals, to two places

Question

You measure 37 textbooks' weights, and find they have a mean weight of 64 ounces. Assume the population standard deviation is 5.8 ounces. Based on this, construct a 90% confidence interval for the true population mean textbook weight.

 

Can anyone assist?

Answer 1

When the population standard deviation is known, the formula for a confidence interval (CI) for a population mean is

 

CI = x +/- z*(σ/√n)

 

where x = sample mean

          z = z-value = 1.645 for 90% Confidence Level

          σ = standard deviation

         '+/-' = + or -

          n is the sample size

z*–values for Various Confidence Levels

Confidence Level z*-value
80%   1.28
90%   1.645 (by convention)
95%   1.96
98%   2.33
99%   2.58

 

Therefore, plugging in values to determine Confidence Interval (CI):

 

 

lower CI = 64 oz - 1.645*(5.8 oz/√37) = 62.43

 

upper CI = 64 oz + 1.645*(5.8 oz/√37) = 62.57

 

 

The confidence interval is from 62.43 to 65.57