Assume that the average gas mileage of all automobiles is 20.2 miles per gallon.

Question

Assume that the average gas mileage of all automobiles is 20.2 miles per gallon. For a random sample of 60 sport utility vehicles (SUVs), the mean gas mileage is 20.0 miles per gallon with a standard deviation of 3.8 miles per gallon. Test the claim that the mean mileage of all SUVs is less than 20.2 miles per gallon. Use a 0.05 significance level.

1. State the null and alternative hypotheses.

2. Find the Z-Score:

3. State the conlusion:

A.

The P-value is greater than greater than the significance level. There is sufficient evidence to support the claim

B.

The P-value is less than or equal to less than or equal to the significance level. There is sufficient evidence to support the claim

C.

The P-value is greater than greater than the significance level. There is not sufficient evidence to support the claim

D.

The P-value is less than or equal toless than or equal to the significance level. There is notsufficient evidence to support the claim

O A. ( B. HOH #20.2 miles per gallon Ha : = 20.2 miles per gallon 0: = 20.2 miles per gallon Ha: > 20.2 miles per gallon Ho: = 20.2 miles per gallon Ha: #20.2 miles per gallon Ho: = 20.2 miles per gallon Ha:

Explanation / Answer

The statistical software output for this problem is:

One sample T summary hypothesis test:
: Mean of population
H0 : = 20.2
HA : < 20.2

Hypothesis test results:

Hence,

1. Hypotheses: Option D is correct.

2. z - score = - 0.41

3. Conclusion: The P-value is greater than the significance level. There is not sufficient evidence to support the claim.

Option C is correct.

Mean Sample Mean Std. Err. DF T-Stat P-value 20 0.49057789 59 -0.40768246 0.3425

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