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 μ1 and μ2 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. (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.
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
(a) Let μ1 and μ2 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.
(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.
Step by step
Solved in 3 steps with 3 images
