Suppose 1 and 2 are true mean stopping distances at 50 mph f

Suppose ?₁ and ?₂ are true mean stopping distances at 50 mph for cars of a certain type equipped with two different types of braking systems. The data follows:

Does the interval suggest that precise information about the value of this difference is available?

Because the interval is so wide, it appears that precise information is available.

Because the interval is so narrow, it appears that precise information is not available.    

Because the interval is so narrow, it appears that precise information is available.

Because the interval is so wide, it appears that precise information is not available.

Solution

The degree of freedom =n1+n2-2=9+9-2=16

Given a=0.05, t(0.025, df=16) =2.12 (from student t table)

So 95% confidecen interval is

(xbar1-xbar2) +/- t*sqrt(s1^2/n1+s2^2/n2)

--> (113.4-129.1) +/- 2.12*sqrt(5.04^2/9+5.39^2/9)

--> (-20.91, -10.49)

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Because the interval is so wide, it appears that precise information is not available.