An insurance company wants to know if the average speed at which men drive cars is greater than that of women drivers. T

[answerhappygod]

An insurance company wants to know if the average speed at which
men drive cars is greater than that of women drivers. The company
took a random sample of 25 cars driven by men on a highway and
found the mean speed to be 70 miles per hour with a standard
deviation of 3.2 miles per hour. Another sample of 16 cars driven
by women on the same highway gave a mean speed of 72 miles per hour
with a standard deviation of 2.5 miles per hour. Assume that the
speeds at which all men and all women drive cars on this highway
are both normally distributed with the same population standard
deviation.
(a) Let μ1μ1 and μ2μ2 be
the population means of driving speed by men and women drivers,
respectively. Find the point estimate for difference between the
mean speeds of men and women drivers. (2
points)
(b) Test at the 1% significance level
whether the mean speed of cars driven by all men drivers on this
highway is greater than that of cars driven by all women
drivers. (4 points)