The table below gives information concerning the gasoline mileage for random samples of trucks of two different types.Find a 95% confidence interval for the difference in the means
-
.
A)(3.68,5.32)
B)(-5,-4)
C)(4,5)
D)(-5.32,-3.68)
E)(20.4,24.9)

Question

The table below gives information concerning the gasoline mileage for random samples of trucks of two different types.Find a 95% confidence interval for the difference in the means 
- 
. 
A)(3.68,5.32) 
B)(-5,-4) 
C)(4,5) 
D)(-5.32,-3.68) 
E)(20.4,24.9)

Quizplus · Accepted Answer

To find the confidence interval for the difference in means, we use the formula:

CI = (x1 - x2) +/- t(alpha/2,df) * sqrt(s1^2/n1 + s2^2/n2)

where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, n1 and n2 are the sample sizes, alpha is the level of significance (0.05 for a 95% confidence interval), df is the degrees of freedom (df = n1 + n2 - 2), and t(alpha/2,df) is the t-critical value.

Plugging in the values from the table, we get:

x1 = 17.5, s1 = 0.707, n1 = 8 
x2 = 22.1, s2 = 0.842, n2 = 12 
df = 8 + 12 - 2 = 18 
t(alpha/2,df) = t(0.025,18) = 2.101

CI = (17.5 - 22.1) +/- 2.101 * sqrt((0.707^2/8) + (0.842^2/12)) 
   = -4.6 +/- 0.820 
   = (-5.42, -3.78)

Therefore, the 95% confidence interval for the difference in means is (-5.32, -3.68). The best choice is D.

The Table Below Gives Information Concerning the Gasoline Mileage for Random