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 35 mothers gave a sample mean of x₁ = 67.17. Another random sample of 27 fathers gave x₂ = 59.85. Assume that σ₁ = 11.06 and σ₂ = 11.13.

(a) Let μ₁ be the population mean of x₁ and let μ₂ be the population mean of x₂. Find a 95% confidence interval for μ₁ – μ₂. (Use 2 decimal places.)

lower limit
upper limit

Answer 1

95% confidence interval for 1 - 2 is

(1 - 2 ) - Z * sqrt( 1 / n1 + 2 / n2) < 1 - 2 < (1 - 2 ) + Z * sqrt( 1 / n1 + 2 / n2)

(67.17 - 59.85) - 1.96 * sqrt( 11.06² / 35 + 11.13² / 27 ) < 1 - 2

< (67.17 - 59.85) + 1.96 * sqrt( 11.06² / 35 + 11.13² / 27 )

1.75 <  1 - 2 < 12.89

Lower limit = 1.75

Upper limit = 12.89