Question

Interval estimates were produced for amount paid for travel by a state's Congressmen in the years 2000 to 2005. Suppose the regression equation for the relationship between trip length x in days and amount paid y in dollars is

ŷ = −669 + 1,178x.

(a) Which interval should be narrower?

The interval estimate of amount paid for an individual 5-day trip by a Congressman in the larger population.

The interval estimate of mean amount for all 5-day trips taken by the larger population of Congressmen.     

(b) How much higher should the center of the interval estimates be for the amount paid for a 10-day trip compared to the amount for a 5-day trip?


(c) Note that the mean trip length was approximately 5 days. Which confidence interval should be narrower?

The interval estimate of mean amount paid for all 10-day trips.

The interval estimate of mean amount paid for all 5-day trips.     

(d) Using the predicted value

ŷ = −669 + 1,178(10) = 11,111,

the spread s = 3,423, and the sample size n = 30, find the interval ŷ ± 2

s

n

. (Round your answers to the nearest whole number.)
(  ,  )

(e) Explain why the interval you constructed in part (d) is not very accurate as a 95% confidence interval for the mean amount paid for a 10-day trip.

The interval is not very accurate because the sample size is too small.

The interval is not very accurate because 10 is too close to the mean trip length, 5 days.     

The interval is not very accurate because 10 is too far from the mean trip length, 5 days.

The interval is not very accurate because the standard deviation is large.

Answer 1

a)

The interval estimate of mean amount for all 5-day trips taken by the larger population of Congressmen.     

b)\

expected change =1178*(10-5)=5890

c)

The interval estimate of mean amount paid for all 5-day trips.     

d)

interval y^ ± 2*s/√n =11111 ± 2*3423/√30 =(9861 , 12361)

e)\

The interval is not very accurate because 10 is too far from the mean trip length, 5 days.