Question

A local environmental group was interested in estimating the total amount (in pounds) of recycled material that is collected weekly from the curbside of households within the Clemson city limits. There are 3500 households in the Clemson city limits. Sixty-four Clemson households were randomly selected and the average weekly amount of curbside recycled material collected from these households was 4 pounds with a standard deviation of 0.5 pound. Construct a 95% confidence interval for the mean amount of recycled material from all households in Clemson.

Answer 1

95% confidence interval for the mean amount of recycled material from all households in Clemson is between a lower limit of 3.875 pounds and an upper limit of 4.125 pounds.

Explanation:

Confidence interval is given as mean +/- margin of error (E)

mean = 4 pounds

sample sd = 0.5 pound

n = 64

degree of freedom = n-1 = 64-1 = 63

confidence level (C) = 95% = 0.95

significance level = 1 - C = 1 - 0.95 = 0.05 = 5%

Critical value (t) corresponding to 63 degrees of freedom and 5% confidence level is 1.9982

E = t×sample sd/√n = 1.9982×0.5/√64 = 0.125 pound

Lower limit of mean = mean - E = 4 - 0.125 = 3.875 pounds

Upper limit of mean = mean + E = 4 + 0.125 = 4.125 pounds

95% confidence interval is (3.875, 4.125)