Question

do Parts (a) and (b)

(A) A police officer in the Lansing Police Department wants to determine with 95% confidence the average number of days it takes for an accident report to be prepared. If he wants to be accurate to within 4 days, how large a sample does he need? (It is thought that the standard deviation is 25 days). The population will consist of 4000 accident reports prepared over 20 years.

(B) Describe two ways to reduce the margin of error when finding the interval estimate for the population mean.

Answer 1

(A) given that margin of error (E) = 4 and standard deviation (SD) = 25

z score for 95% confidence level is 1.96(using z table)

sample size n =((z*SD)/E)^2

= ((1.96*25)/4)^2

= (12.25)^2

= 150.0625

= 150(rounded to nearest integer)

(B) Margin of error is given as

z is critical value, sigma is standard deviation and n is sample size

decreasing the critical value or confidence level will reduce the margin of error

decreasing the standard deviation will reduce the margin of error

increasing the sample size will reduce the margin of error