A study of parental empathy for sensitivity cues and baby temperament (higher scores mean more empathy) was performed. Letx₁be a random variable that represents the score of a mother on an empathy test (as regards her baby). Letx₂be the empathy score of a father. A random sample of34mothers gave a sample mean ofx₁=67.17. Another random sample of38fathers gavex₂=61.72. Assume that₁=11.48and₂=11.34.

(a) Let₁be the population mean ofx₁and let₂be the population mean ofx₂. Find a90%confidence interval for₁-₂. (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 the90%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.