Question

The mayor is interested in finding a 98% confidence interval for the mean number of pounds of trash per person per week that is generated in the city. The study included 240 residents whose mean number of pounds of trash generated per person per week was 34.5 pounds and the standard deviation was 7.8 pounds. Round answers to 3 decimal places where possible.

a. To compute the confidence interval use a  z or t  distribution.

b. With 98% confidence the population mean number of pounds per person per week is between  and pounds.

c. If many groups of 240 randomly selected members are studied, then a different confidence interval would be produced from each group. About  percent of these confidence intervals will contain the true population mean number of pounds of trash generated per person per week and about  percent will not contain the true population mean number of pounds of trash generated per person per week.

Answer 1

a)
Given
X̅ = 34.5           ....... Sample Mean
n = 240           ....... Sample Size
s = 7.8           ....... Sample Standard Deviation

Since the population standard deviation is unknown, we use the t-distribution

For 98% Confidence interval

α = 0.02,      α/2 = 0.01
From t tables of Excel function T.INV.2T (α, degrees of freedom) we find the t value
t = T.INV.2T (0.02, 239) = 2.342
We take the positive value of t

Confidence interval is given by

= (33.321, 35.679)

98% Confidence interval is (33.321, 35.679)

b) With 98% confidence the population mean number of pounds per person per week is between 33.321 and 35.679 pounds.

c) About 98% percent of these confidence intervals will contain the true population mean number of pounds of trash generated per person per week and about 2% percent will not contain the true population mean number of pounds of trash generated per person per week.