Question

The 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 26 n 26 35 25 IH 15 automatic manual Hwy MPG 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 O 98% of manual and automatic cars will have a difference in highway mileage that falls 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 Does your confidence interval provide significant evidence for a difference in the highway fuel efficiency of automatic versus manual cars? Explain. yes, since highway mileage cannot be negative O no, since negative highway mileage doesn't make sense O no, since 0 is not contained within our confidence interval O yes, since 0 is not contained within our confidence interval

Answer 1

Result:

Let group1 = manual and group2 = automatic

Lower bound: 1.53

Upper bound: 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.

Yes, since 0 is not contained within our confidence interval.

$CI = ( \bar x_1 - \bar x_2) \pm t*se$

$se= \sqrt{ \frac{(n_1 - 1) s_1^2 + (n_2 - 1) s_2^2} {(n_1 +n_2 -2)} *{(\frac{1}{n_1} + \frac{1}{n_2})}}$

1 Sample
Sample Size	26
Sample Mean	27.88
Sample Standard Deviation	5.01
2 Sample
Sample Size	26
Sample Mean	22.92
Sample Standard Deviation	5.29
Intermediate Calculations
Population 1 Sample Degrees of Freedom	25
Population 2 Sample Degrees of Freedom	25
Total Degrees of Freedom	50
Pooled Variance	26.5421
Standard Error	1.4289
Difference in Sample Means	4.9600

Confidence Interval Estimate
for the Difference Between Two Means
Data
Confidence Level	98%
Intermediate Calculations
Degrees of Freedom	50
t Value	2.4033
Interval Half Width	3.4340
Confidence Interval
Interval Lower Limit	1.5260
Interval Upper Limit	8.3940