Question

he table provides summary statistics on highway fuel economy of cars manufactured in 2012 (from Exercise 5.32). Use these statistics to calculate a 98% confidence interval for the difference between average highway mileage of manual and automatic cars, and interpret this interval in the context of the data.

	Hwy MPG, Automatic	Hwy MPG, Manual
Mean	22.92	27.88
SD	5.29	5.01
n	26	26

lower bound:  mpg (please round to two decimal places)
upper bound:  mpg (please round to two decimal places)
Interpret your confidence interval in the context of the problem:

• We can be 98% confident that our confidence interval contains the difference in average highway mileage of the cars in our sample is contained within our confidence interval
• We can be 98% confident that the difference in average highway mileage of manual and automatic cars is contained within our confidence interval
• 98% of manual and automatic cars will have a difference in highway mileage that falls within our confidence interval

Does your confidence interval provide significant evidence for a difference in the highway fuel efficiency of automatic versus manual cars? Explain.

• no, since 0 is not contained within our confidence interval
• no, since negative highway mileage doesn't make sense
• yes, since highway mileage cannot be negative
• yes, since 0 is not contained within our confidence interval

LicensePoints possible: 3
This is attempt 1 of 4.

Answer 1

For Manual : x̅1 = 27.88, s1 = 5.01, n1 = 26  

For Automatic : x̅2 = 22.92, s2 = 5.29, n2 = 26  

df = ((s1²/n1 + s2²/n2)²)/[(s1²/n1)²/(n1-1) + (s2²/n2)²/(n2-1) ] = 49.8529 = 50  

98% Confidence interval for the difference :  

At α = 0.02 and df = 50, two tailed critical value, t_c = T.INV.2T(0.02, 50) =    2.403

Lower Bound = (x̅1 - x̅2) - t_c*√(s1²/n1 +s2²/n2)

= (27.88 - 22.92) - 2.403*√(5.01²/26 + 5.29²/26) = 1.53

Upper Bound = (x̅1 - x̅2) + t_c*√(s1²/n1 +s2²/n2)

= (27.88 - 22.92) + 2.403*√(5.01²/26 + 5.29²/26) = 8.39

--

We can be 98% confident that the difference in average highway mileage of manual and automatic cars is contained within our confidence interval.

--

no, since 0 is not contained within our confidence interval.