Ten randomly selected cars were filled with either regular or premium gas (the decision was made based on a coin toss) and then driven on the freeway for the entirety of the tank of gas. The next day, each car was filled with whichever type of gas that was not used the previous day and then driven on the freeway for the entirety of the tank of gas. The mileage for each day was recorded and is summarized in the table below. MPG of 10 cars (regular/premium): 13/19, 20/22, 21/24, 23/25, 22/25, 27/26, 25/26, 27/28, 28/32, 22/24. Car 1 Car 2 Car 3 Car 4 Car 5 Car 6 Car 7 Car 8 Car 9 Car 10 Regular 16 20 21 23 22 27 25 27 28 22 Premium 19 22 24 25 25 26 26 28 32 24 You will be constructing a 90% confidence interval estimate of the difference between the mean efficiency of the car using regular and premium gas. You may assume that both samples are drawn from normally distributed populations. The mean of the differences between the two samples is . Round your answer to 3 decimal places. The standard deviation of the differences between the two samples is . Round your answer to 3 decimal places. The right hand critical value is . Round to 3 decimal places. The margin of error, rounded to 3 decimal places, is . Construct the 90% confidence interval estimate mean difference between the mileage from cars using regular and premium gas. Round your answer to 2 decimal places. _______ < difference between the means < _______ Is premium gas really more efficient? Justify your answer with statistics.
Ten randomly selected cars were filled with either regular or premium gas (the decision was made based on a coin toss) and then driven on the freeway for the entirety of the tank of gas. The next day, each car was filled with whichever type of gas that was not used the previous day and then driven on the freeway for the entirety of the tank of gas. The mileage for each day was recorded and is summarized in the table below.
MPG of 10 cars (regular/premium): 13/19, 20/22, 21/24, 23/25, 22/25, 27/26, 25/26, 27/28, 28/32, 22/24.
| Car 1 | Car 2 | Car 3 | Car 4 | Car 5 | Car 6 | Car 7 | Car 8 | Car 9 | Car 10 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Regular | 16 | 20 | 21 | 23 | 22 | 27 | 25 | 27 | 28 | 22 |
| Premium | 19 | 22 | 24 | 25 | 25 | 26 | 26 | 28 | 32 | 24 |
You will be constructing a 90% confidence
You may assume that both samples are drawn from
The mean of the differences between the two samples is . Round your answer to 3 decimal places.
The standard deviation of the differences between the two samples is . Round your answer to 3 decimal places.
The right hand critical value is . Round to 3 decimal places.
The margin of error, rounded to 3 decimal places, is .
Construct the 90% confidence interval estimate mean difference between the mileage from cars using regular and premium gas. Round your answer to 2 decimal places.
_______ < difference between the means < _______
Is premium gas really more efficient? Justify your answer with statistics.
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