Question

A study of parental empathy for such a baby temperament ( higher scores mean more empathy) was performed. Let X1 a random variable that represents a 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 40 mothers gave a sample mean of x1= 68.36. Another random sample of 39 fathers gave x2 = 59.51. Assume standard deviation 1 = 11.76 and standard deviation 2= 11.83.

(a) u1 be the population mean of x1 and let u2 be the population mean of x2. find a 90% confidence interval for u1-u2.

lower limit-

upper limit-

(b) examine the confidence interval and explain what it means in the context of this problem. Does the confidence interval contain all positive, all negative, or both positive and negative numbers?

Answer 1

(a)

Lower Limit - 4.431

Upper Limit - 13.269

We need to construct the 90% confidence interval for the difference between the population means μ1​−μ2​, for the case that the population standard deviations are not known. The following information has been provided about each of the samples:

(b)

Therefore, based on the data provided, the 90% confidence interval for the difference between the population means μ1​−μ2​ is 4.431<μ1​−μ2​<13.269, which indicates that we are 90% confident that the true difference between population means is contained by the interval (4.431,13.269)

The confidence interval contains all positive numbers.

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