Question

44 people who own a car in California are randomly selected by an insurance company. The number of miles the car is driven during the year is recorded. The summary statistics are: x̅ = 13,961 miles, s = 4,672.

Construct a 97 percent confidence interval for the mean, μ, amount of miles each car in California is driven. List the margin of error

Answer 1

= 4,672 Allo M44. sol Given that 44 people who own a car in California are randomly selected by an insurance company, and the number of miles the car ię driven during the year if record. so 7=13,9ci miles Now, the 97% confidence interval for by t statistic (because populalion standard deviation is unknown ED *+ 3.244 s? II (Xo - aj? يل n Where n-l s²= I ns². n-l So so equation becomes F + 2.244 in 8 Folin-1 Ã + 2,2442 JM-1) putting the value off and s. we have, 4672 13,961 I 2.244x N44-1 13961 t 1598.7907. so required confidence interval= = (13961–1598.7901, 13961+ 1598.7401) = (12 362-2099 , 15559.7901) -

s Also margin of error = tala * J X = tolg s dhal 1 8=4672, n=44, Here tale 32.244, SO margin of error = 2,2444 4672 44-) = 2.244X 4672 43 =1598.7901,