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NOTHER 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 32 mothers gave a sample mean of x, = 68.36. Another random sample of 32 fathers gave x, = 59.38. Assume that o, = 11.55 and o, = 11.45. (a) Let u, be the population mean of x, and let /, be the population mean of x, . Find a 99% confidence interval for , - ,. (Round your answers to two 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's res for mothers compared with those for fathers at the 99% confidence level? O Because the interval contains only positive numbers, we can say that the mothers have a gher mean empathy score. O 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. O Because the interval contains only negative numbers, we can say that the fathers have a higher mean empathy score