A study of parental empathy for sensitivity cues and baby te

A study of parental empathy for sensitivity cues and baby temperament (higher scores mean more empathy) was performed. Let X1 be a random variable that represents the score of a mother on an empathy test (as regards her baby). Let x2 be the empathy score of a father. A random sample of 33 mothers gave a sample mean of X1 = 67.85. Another random sample of 27 fathers gave x2 60.19. Assume that Sigma 1= 10.78 and sigma2 = 12.32. (a) Let mu 1 be the population mean of x1 and let mu 2 be the population mean of x2. Find a 95% confidence interval for mu 1- mu 2. (Use 2 decimal places.)

Solution

Given a=1-0.95=0.05, Z(0.025) = 1.96 (from standard normal table)

So the lower limit is

(xbar1-xbar2) - Z*sqrt(s1^2/n1+s2^2/n2)

=(67.85-60.19)-1.96*sqrt(10.78^2/33+12.32^2/27)

=1.73

So the upper limit is

(xbar1-xbar2) + Z*sqrt(s1^2/n1+s2^2/n2)

=(67.85-60.19) + 1.96*sqrt(10.78^2/33+12.32^2/27)

=13.59