Question

    Records of 40 used passenger cars and 40 used pickup trucks were randomly sampled to investigate

          whether there was any significant difference in the mean time in years that they were kept by the original

          owner before being sold.  For the sampled cars, the mean was 5.3 years with a standard deviation of 2.2

          years.  For the sampled pickup trucks, the mean was 7.1 years with a standard deviation of 3.0 years.  

          (Assume that the two samples are independent.)

a)  Construct and interpret the 90% confidence interval estimate of the difference between the mean time for all passenger cars and the mean time for all pickup trucks.

b)  Does there appear to be a significant difference between the two population means?  Is one higher than

               the other?  If so, who keeps their vehicles longer?

Answer 1

: mean time for all passenger cars

: mean time for all pickup trucks

Given,

Passengers cars : Sample 1

Sample size : n1=40

Sample mean: = 5.3

Sample standard deviation s1:  2.2

Pickup trucks : Sample 2

Sample size : n2=40

Sample mean: = 7.1

Sample standard deviation s2:  2.2

for 90% confidence level = (100-90)/100=0.10 ; /2 =0.10/2 = 0.05

a)

Method 1:

Population Standard deviations not equal assumed:

Formula for Confidence Interval for Difference in two Population means

90% confidence interval estimate of the difference between the mean time for all passenger cars and the mean time for all pickup trucks

90% confidence interval estimate of the difference between the mean time for all passenger cars and the mean time for all pickup trucks = (-2.7805, -0.8195)

b)

As '0' is outside the confidence interval ,there appears to be a significant difference between the two population means.

Is one higher than the other? yes; mean time for all pickup trucks higher

And the confidence interval is : for ( mean time for all passenger cars - mean time for all pickup trucks) and both the limits are negative,

( mean time for all passenger cars - mean time for all pickup trucks) < 0

i.e

mean time for all passenger cars < mean time for all pickup trucks

i.e pickup trucks owners keep their vehicles longer

-------------------------------------------------

Method 2:

Population Standard deviations equal assumed:

Formula for Confidence Interval for Difference in two Population means

90% confidence interval estimate of the difference between the mean time for all passenger cars and the mean time for all pickup trucks

90% confidence interval estimate of the difference between the mean time for all passenger cars and the mean time for all pickup trucks = (-2.7792,-0.8208)

b)

As '0' is outside the confidence interval ,there appears to be a significant difference between the two population means.

Is one higher than the other? yes; mean time for all pickup trucks higher

And the confidence interval is : for ( mean time for all passenger cars - mean time for all pickup trucks) and both the limits are negative,

( mean time for all passenger cars - mean time for all pickup trucks) < 0

i.e

mean time for all passenger cars < mean time for all pickup trucks

i.e pickup trucks owners keep their vehicles longer