# The data accompanying this exercise show miles per gallon (mpg) for 25 cars. 97 117 93...

###### 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; HA: σ2 ≠ 62(mpg)2

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

• H0: σ2 ≥ 62(mpg)2; HA: 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.

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