The data accompanying this exercise show miles per gallon (mpg) for 25 cars.
97 |
117 |
93 |
79 |
97 |
87 |
78 |
83 |
94 |
96 |
102 |
98 |
82 |
96 |
113 |
113 |
111 |
90 |
101 |
99 |
112 |
89 |
92 |
96 |
98 |
a. Select the null and the alternative hypotheses in order to test whether the variance differs from 62 mpg^{2}.
H_{0}: σ^{2} = 62(mpg)^{2}; H_{A}: σ^{2} ≠ 62(mpg)^{2}
H_{0}: σ^{2} ≤ 62(mpg)^{2}; H_{A}: σ^{2} > 62(mpg)^{2}
H_{0}: σ^{2} ≥ 62(mpg)^{2}; H_{A}: σ^{2} < 62(mpg)^{2}
b. Assuming that mpg is normally distributed, calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)
c. Find the p-value.
p-value < 0.01
0.01 ≤ p-value < 0.02
0.02 ≤ p-value < 0.05
0.05 ≤ p-value < 0.10
p-value ≥ 0.10
d. Make a conclusion at α = 0.01.
Reject H_{0}; we can say that the variance differs from 62.
Reject H_{0}; we cannot say that the variance differs from 62.
Do not reject H_{0}; we can say that the variance differs from 62.
Do not reject H_{0}; we cannot say that the variance differs from 62.