In: Statistics and Probability
In 2008, a small dealership leased 21 Subaru Outbacks on 2-year leases. When the cars were returned in 2010, the mileage was recorded (see below). |
40,003 | 24,939 | 14,329 | 17,380 | 44,741 | 44,554 | 20,229 |
33,370 | 24,220 | 41,702 | 58,328 | 35,831 | 25,790 | 28,983 |
25,066 | 43,357 | 23,993 | 43,557 | 53,670 | 31,811 | 36,709 |
(a) |
Is the dealer's mean significantly greater than the national average of 30,162 miles for 2-year leases? Using the 10 percent level of significance, choose the appropriate hypothesis. |
a. | H0: μ ≤ 30,162 miles vs. H1: μ > 30,162 miles, reject H0 if tcalc > 1.3250 |
b. | H0: μ ≥ 30,162 miles vs. H1: μ > 30,162 miles, reject H0 if tcalc > 1.3250 |
c. | H0: μ ≤ 30,162 miles vs. H1: μ < 30,162 miles, reject H0 if tcalc > 1.3250 |
d. | H1: μ ≤ 30,162 miles vs. H0: μ > 30,162 miles, reject H0 if tcalc > 1.3250 |
|
(b) |
Calculate the test statistic. (Round your answer to 2 decimal places.) |
Test statistic |
(c) |
The dealer's cars show a significantly greater mean number of miles than the national average at the 10 percent level. |
|
X : The mileage of care (in miles)
n=21
Sr. No. | X | X^2 |
1 | 40003 | 1600240009 |
2 | 24939 | 621953721 |
3 | 14329 | 205320241 |
4 | 17380 | 302064400 |
5 | 44741 | 2001757081 |
6 | 44554 | 1985058916 |
7 | 20229 | 409212441 |
8 | 33370 | 1113556900 |
9 | 24220 | 586608400 |
10 | 41702 | 1739056804 |
11 | 58328 | 3402155584 |
12 | 35831 | 1283860561 |
13 | 25790 | 665124100 |
14 | 28983 | 840014289 |
15 | 25066 | 628304356 |
16 | 43357 | 1879829449 |
17 | 23993 | 575664049 |
18 | 43557 | 1897212249 |
19 | 53670 | 2880468900 |
20 | 31811 | 1011939721 |
21 | 36709 | 1347550681 |
Total | 712562 | 26976952852 |