“Parental Sensitivity to Infant Cues: Similarities and Differences Between Mothers and Fathers” by M. V. Graham (Journal of Pediatric Nursing, Vol. 8, No. 6) reports a study of parental empathy for sensitivity cues and baby temperament (higher scores mean more empathy). 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 32 mothers gave a sample mean of x̅₁ = 69.44. Another random sample of 32 fathers gave x̅₂ = 59. Assume that s₁ = 11.69 and s₂ = 11.60.

(a) Check Requirements Which distribution, normal or Student’s t, do we use to approximate the x̅₁ – x̅₂ distribution? Explain.

(b) Let m1 be the population mean of x₁ and let m₂ be the population mean of x₂. Find a 99% con­fidence interval for m₁ – m₂.

(c) Interpretation 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?