SOLUTION: A small dealership leased 21 Suburu Outbacks on 2-year leases. Two years later, when the cars were returned, the mileage was recorded (see below). Is the dealer’s mean significa

Question 1188602: A small dealership leased 21 Suburu Outbacks on 2-year leases. Two years later, when the cars were returned, the mileage was recorded (see below). Is the dealer’s mean significantly different from the national average of 30,000 miles for 2-year leased vehicles, using the 10 percent level of significance? (a) What is the appropriate testing method? Please write down each step of hypothesis testing for this case. (b) Please solve this problem and show the process and the output file. (20 points total)
40060, 24960, 14310, 17370, 44740, 44550, 20250,
33380, 24270, 41740, 58630, 35830, 25750, 28910,
25090, 43380, 23940, 43510, 53680, 31810, 36780

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the population mean is assumed to be 30,000 (national average).
the population standard deviation is not known, therefore the sample standard deviation is used instead and the t-score is used instead of the z-score.

here's a reference on choosing between z-score and t-score.
https://math.stackexchange.com/questions/1817980/how-to-know-when-to-use-t-value-or-z-value

the statistics for the sample given was determined by use of the online descriptive statistics calculator at https://www.calculatorsoup.com/calculators/statistics/descriptivestatistics.php

from this calculator, it was determined that:

the sample mean was 33949.5238.
the sample standard deviation was 11866.174.
the sample size was 21.

10% level of significance equals 90% confidence interval.
two tail 90% confidence interval has 5% tail on each end.
critical t-score with 20 degrees of freedom (sample size minus 1) = plus or minus 1.742718218.

this was determined through the use of the ti-84 plus scientific calculator, but could also have been determined through the online calculator found at https://www.omnicalculator.com/statistics/critical-value

at critical t-score of plus or minus 1.742718218, use the t-score formula to find the raw score.

that formula is t = (x - m) / s
t is the t-score.
x is the sample mean.
m is the assumed population mean.
s is the standard error.

the standard error is the standard deviation of the distribution of sample means.
the formula for that is:
s = standard deviation / square root of sample size.
that becomes:
s = 11866.174 / sqrt(21) = 2589.411455.

the test t-score was determined to be:

t = (33949.5238 - 30000) / 2589.41455 = 1.525257437.

since this was less than the critical t-score of 1.742718218, the results of the test were not significant, indicating there was not enough evidence to say that the mean scores for the dealership were different than the mean scores of the population.

here's a display of the descriptive statistics for the sample.

here's a display of the results of using the online critical t-value calculator.

RELATED QUESTIONS
A small dealership leased 21 Suburu Outbacks on 2-year leases. Two years later, when the... (answered by Boreal)

I'm dying a slow death in statistics. Please help! In 2004, a small dealership leased (answered by stanbon)

Please help. In 2004, a small dealership leased 21 Chevy impalas on 2-year leases.... (answered by stanbon)

In 2004, a small dealership leased 21 Chevy impalas on 2-year leases. When the cars were... (answered by stanbon)

Last year at a certain car dealership the ratio of cars to suv's sold was 5 to 3. If 400... (answered by rfer,drj)

Most four-year automobile leases allow up to 77,000 miles. If the lessee goes beyond this (answered by stanbon)

 Automobile Leasing A car leasing agency purchases new cars each year for use in the... (answered by Theo)

Most four-year automobile leases allow up to 77,000 miles. If the lessee goes beyond this (answered by ewatrrr)

Algebra Question...a car dealership sells cars and trucks in a ratio of 7 to 5. Last... (answered by rfer)