College statistics

Question

The mayor is interested in finding a 90% confidence interval for the mean number of pounds of trash per person per week that is generated in city. The study included 169 residents whose mean number of pounds of trash generated per person per week was 35.8 pounds and the standard deviation was 6.1 pounds.

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

b. With 90% confidence the population mean number of pounds per person per week is between  and pounds. 

c. If many groups of 169 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

The sample size is very large so you can use the z distribution

90% CI = sample mean +/- critical z * sample standard deviation/square root(sample size)

critical z for 90% CI is 1.645.

Ninety percent of all confidence intervals will contain the true population mean; ten percent will not.