A study of parental empathy for sensitivity cues and baby temperament (higher scores mean more empathy) was performed. Let x, be a random variable that represents the score of a mother on an empathy test (as regards her baby). Let x, be the empathy score of a father. A random sample of 25 mothers gave a sample mean of x, = 67.00. Another random sample of 29 fathers gave x2 = 61.72. Assume that of = 11.55 and 02 = 12.39. (a) Let , be the population mean of x, and let uz be the population mean of X2. Find a 95% confidence interval for , - U2. (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 95% 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. O 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. US ) 9 9 6:58