A study of parental empathy for sensitivity cues and baby temperament (higher sc
ID: 3134509 • Letter: A
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 27 mothers gave a sample mean of x1 = 68.19. Another random sample of 30 fathers gave x2 = 61.55. Assume that 1 = 11.20 and 2 = 11.34. (a) Let 1 be the population mean of x1 and let 2 be the population mean of x2. Find a 90% confidence interval for 1 – 2. (Use 2 decimal places.)
Explanation / Answer
Given that n1 =27n2 = 30X1=68.19X2= 61.551 = 11.202 = 11.34
S.E(X1 - X2) = 1 2/n1) + 2 2/n2)
=125.4400/27 +128.5956/30
=2.9887
90% confidence interval for µ1-µ2
X1 - X2 ± 1.645 S.E(X1 - X2)
68.19-61.55± 1.645 *2.9887
6.6400 ± 1.645*2.9887
[1.7236 ,11.5564]
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