Question

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 29 mothers gave a sample mean of x1 = 67.68. Another random sample of 34 fathers gave x2 = 60.36. Assume that σ1 = 10.85 and σ2 = 10.92.

(a) Let μ1 be the population mean of x1 and let μ2 be the population mean of x2. Find a 99% confidence interval for μ1 – μ2. (Use 2 decimal places.)

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? What does this tell you about the relationship between average empathy scores for mothers compared with those for fathers at the 99% confidence level?

- Because the interval contains only positive numbers, we can say that the mothers have a higher mean empathy score.

- Because the interval contains both positive and negative numbers, we can not say that the mothers have a higher mean empathy score.

- We can not make any conclusions using this confidence interval.

- Because the interval contains only negative numbers, we can say that the fathers have a higher mean empathy score.

Answer 1

from above

lower limit =0.23

upper limit=14.41 (try 14.42 if this comes wrong due to rounding error)

Because the interval contains only positive numbers, we can say that the mothers have a higher mean empathy score.