let x1 be a random variable that represents the score of amother on an empathy t
ID: 2954222 • Letter: L
Question
let x1 be a random variable that represents the score of amother on an empathy test (as regards her baby). let x2 be theempathy score of a father. a random sample of 32 mothers gave asample mean of x bar1 = 69.44. another random sample of 32 fathersgave x bar2= 59. assume that 1= 11.69 and 2 =11.60.a.) let 1 be the population mean of x1 and let 2be the population mean of x2. find a 99%(2.58) confidence intervalfor 1- 2. b.) examine the confidence interval and explain what it meansin the context of this problem. does the confidence intervalcontain all positive, all negative, or both positive and negativenumbers? what does this tell you about the relationship betweenaverage empathy scores for mothers cmopared wtih those for fathersat the 99% confidence interval? let x1 be a random variable that represents the score of amother on an empathy test (as regards her baby). let x2 be theempathy score of a father. a random sample of 32 mothers gave asample mean of x bar1 = 69.44. another random sample of 32 fathersgave x bar2= 59. assume that 1= 11.69 and 2 =11.60.
a.) let 1 be the population mean of x1 and let 2be the population mean of x2. find a 99%(2.58) confidence intervalfor 1- 2. b.) examine the confidence interval and explain what it meansin the context of this problem. does the confidence intervalcontain all positive, all negative, or both positive and negativenumbers? what does this tell you about the relationship betweenaverage empathy scores for mothers cmopared wtih those for fathersat the 99% confidence interval?
Explanation / Answer
Given n1=32, xbar1=69.44, 1=11.69 n2=32,xbar2=59, 2=11.6 =0.01, Z(0.005)=2.58 (check normal table) The 99% CI is (xbar1 - xbar2) ± Z*(1^2/n1+2^2/n2) --> (69.44-59) ± 2.58*sqrt(11.69^2/32 + 11.6^2/32) --> ( 2.93, 17.95)
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