Two types of flares are tested for their burning times (in minutes) and sample results are given below. $\text{ Brand }\mathrm{X}$ $\text{ Brand }\mathrm{Y}$ n = 35 n = 40 $\overline{x}$ = 19.4 $\overline{x}$ = 15.1 s = 1.4 s = 0.8
Construct a 95% confidence interval for the difference $$\mu \mathrm{X}$$ - $\mu Y$ based on the sample data.

A) (3.5,5.1)
B) (3.8,4.8)
C) (3.6,5.0)
D) (-4.7,-3.9)
E) (3.2,5.4)

To construct the confidence interval for the difference between two means, we use the formula:
(mean1 - mean2) ± t_critical * sqrt((s1^2 / n1) + (s2^2 / n2))
where mean1 and mean2 are the sample means, s1 and s2 are the sample standard deviations, n1 and n2 are the sample sizes, and t_critical is the critical value from the t-distribution with (n1 + n2 - 2) degrees of freedom for a 95% confidence interval (t_critical = 2.021).

Plugging in the given values, we get:
(19.4 - 15.1) ± 2.021 * sqrt((1.4^2 / 35) + (0.8^2 / 40))
= 4.3 ± 0.494
= (3.806, 4.794)

Therefore, the best choice is B, which matches this interval.