Question

1. The driver of a Hyundai Accent takes 12 long trips after filling their car with premium gasoline, and 14 long trips after filling their car with unleaded gasoline. In a hypothesis test to see if there is evidence of a difference in average fuel economy, the p-value is found to be .261 The sample average fuel economy is slightly better for the premium trips (36.3 miles per gallon vs. 35.9 miles per gallon), but premium gasoline is more expensive than unleaded by 40 cents per gallon. Explain your answer. The result of this study is:

1. neither statistically significant nor practically significant.
2. not statistically significant, but it is practically significant.
3. statistically significant and practically significant.
4. statistically significant, but it is not practically significant.

1. It is believed that the average commuter in the Los Angeles area drives more miles per day than the average commuter in San Francisco. A 95% confidence interval for the difference in mean daily miles driven was found to be (-3.53, 12.73), and a 90% confidence interval was found to be (-2.22, 142). Based on those confidence intervals, what can we say about the p-value of a hypothesis test for a difference of means? Explain your answer

1. The p-value is less than .05.
2. The p-value is between .05 and .10.
3. The p-value is greater than .10.
4. The p-value is either less than .05 or greater than .10, but there is not enough information to determine which of those statements is accurate.

Answer 1

Solution:-

1) (b) The result of this study is not statistically significant, but it is practically significant.

Since the p-value is 0.261 greater than 0.05, hence we fail to reject the null hypothesis.

2) (c) The p-value is greater than 0.10.

Since both the confidence interval 90% and 95% contains 0, hence p-value must be greater than 0.10.