Question

Assume that the speeds at which all men and all women drive cars on this highway are both approximately normally distributed with unknown and unequal population standard deviations. a. Construct a 98% confidence interval for the difference between the mean speeds of cars driven by all men and all women on this highway. b. Test at a 1% significance level whether the mean speed of cars driven by all men drivers on this highway is higher than that of cars driven by all women drivers. c. Suppose that the sample standard deviations were 1.9 and 3.4 miles per hour, respectively. Redo parts a and b. Discuss any changes in the results.

n1 = 27 n2= 18 x1 = 72 x2 = 68 s1 = 2.2 s2 = 2.5

Answer 1

a)

t valuee at 98% = 2.5669

CI = (x1 -x2) +/- t *sqrt(s1^2/n1+s2^2/n2)
= (72 - 68) +/- 2.5669 *sqrt(2.2^2/27 + 2.5^2/18)
= (2.1375,5.8625)

b)

H0 : mu1 = mu2
Ha: mu1 > mu2

test statistics:

t = (x1 -x2)/sqrt(s1^2/n1+s2^2/n2)
=(72 - 68) /sqrt(2.2^2/27 + 2.5^2/18)
= 5.5128

p value = 0.00001

Reject H0

c)

t valuee at 98% = 2.5669

CI = (x1 -x2) +/- t *sqrt(s1^2/n1+s2^2/n2)
= (72 - 68) +/- 2.5669 *sqrt(1.9^2/27 + 3.4^2/18)
= (1.7389,6.2611)

b)

H0 : mu1 = mu2
Ha: mu1 > mu2

test statistics:

t = (x1 -x2)/sqrt(s1^2/n1+s2^2/n2)
= (72 - 68) /sqrt(1.9^2/27 + 3.4^2/18)
= 4.5410

p value = 0.00001

Reject H0