Do cars really get better mileage per gallon on the highway? The table shows results from a study of the MPG (miles per gallon) of cars both in the city and on the highway. Assume that the two samples are randomly selected, independent, the population standard deviations are not know and not considered equal. At the 0.1 significance level, test the claim that the mpg on the highway is better than in the city.
Do cars really get better mileage per gallon on the highway?
The table shows results from a study of the MPG (miles per gallon) of cars both in the city and on the highway. Assume that the two samples are randomly selected, independent, the population standard deviations are not know and not considered equal. At the 0.1 significance level, test the claim that the mpg on the highway is better than in the city.
MPG on the Highway
| 35.6 | 34.3 | 32.2 | 33.9 |
| 31.1 | 27.1 | 33.3 | 33.4 |
| 29.3 | 33.5 | 31.4 | 33.2 |
| 33.5 | 30.8 | 33.8 |
MPG in the City
| 26.4 | 25.3 | 18.6 | 25.6 |
| 24.7 | 24.6 | 25.1 | 22.4 |
| 29.3 | 23.7 | 23.4 | 22 |
| 24 | 23.6 | 25.5 |
What are the correct hypotheses? (Select the correct symbols and use decimal values not percentages.)
H0: Select an answer p x̄₁ p₁ σ₁² μ₁ μ₂ μ μ(Highway) x̄₂ p̂₁ s₁² p₂ ? ≤ ≠ < ≥ = > Select an answer p₁ p₂ p̂₁ μ(City) μ μ₁ μ₂ x̄₁ x̄₂ s₁² σ₁² p
H1: Select an answer p₂ μ(Highway) p̂₂ σ₂² x̄₁ x̄₂ s₂² μ₁ μ₂ μ p₁ p ? < ≠ = ≥ ≤ > Select an answer p₂ p₁ μ₁ σ₁² μ(City) p x̄₁ μ x̄₂ p̂₁ s₁² μ₂
Original Claim = Select an answer H₀ H₁
df =
Based on the hypotheses, find the following:
Test Statistic = (Round to three decimal places.)
Critical value(s) = (Round to three decimal places.)
Shade the sampling distribution curve with the correct critical value(s) and shade the critical regions. The arrows can only be dragged to t-scores that are accurate to 1 place after the decimal point (these values correspond to the tick marks on the horizontal axis). Select from the drop down menu to shade to the left, to the right, between or left and right of the t-score(s).
Shade: Left of a valueRight of a valueBetween two values2 regions. Click and drag the arrows to adjust the values.
Decision: Select an answer Accept the null hypothesis Fail to reject the null hypothesis Reject the null hypothesis Accept the alternative hypothesis .
Conclusion: Select an answer The sample data supports There is sufficient evidence to warrant rejection of There is not sufficient evidence to warrant rejection of There is not enough evidence to support the claim that the mpg on the highway is better than in the city.
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