Question

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 mpg².

• H₀: σ² = 62(mpg)²; H_A: σ² ≠ 62(mpg)²

• H₀: σ² ≤ 62(mpg)²; H_A: σ² > 62(mpg)²

• H₀: σ² ≥ 62(mpg)²; H_A: σ² < 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 H₀; we can say that the variance differs from 62.

• Reject H₀; we cannot say that the variance differs from 62.

• Do not reject H₀; we can say that the variance differs from 62.

• Do not reject H₀; we cannot say that the variance differs from 62.

Answer 1

Y = 25 7 = Exi 96.52 2413 25 2 Ex - x)² 114.427 nel 2 Ho 62 # 62 b) Test statistic ܀ ܝܗ x² (n-1) s² 2 (25-1) (114.427) 62 z² 22 44-2943 44. 294 P-value 11 0.00705 P-value 0.01 a Since is p-value less than alpha Ho can Reject varionce say that the differs from 62.