Question

A sample of 10 diesel trucks were run both hot and cold to estimate the difference in fuel economy. The results, in mpg, are presented in the following table.

Truck	Hot	Cold
1	4.56	4.26
2	4.46	4.08
3	6.49	5.83
4	5.37	4.96
5	6.25	5.87
6	5.90	5.32
7	4.12	3.92
8	3.85	3.69
9	4.15	3.74
10	4.69	4.19

Let μXμX represent the population mean for hot engines and let μYμY represent the population mean for cold engines. Find a 98% confidence interval for the difference μD=μX−μYμD=μX−μY. Round the answers to three decimal places.

Answer 1

Using Excel we get, sample mean and sample standard deviation of the difference between Hot engines and Cold engines are,

sample mean = 0.3980 and

sample standard deviation (Sd) = 0.1558

Degrees of freedom = 10 - 1 = 9

Using t-table we get, t-critical value at significance level of 0.02 with 9 degrees of freedom is,

The 98% confidence interval for the difference μD = μX - μY is,

Therefore, required confidence interval is (0.259, 0.537)