A questionnaire is developed to assess women\'s and men\'s attitudes toward usin
ID: 3074116 • Letter: A
Question
A questionnaire is developed to assess women's and men's attitudes toward using animals in research. One question asks whether animal research is wrong and is answered on a 7-point scale. Assume that in the population, the mean for women is 3, the mean for men is 2, and the standard deviation for both groups is 1.5. Assume the scores are normally distributed. If 12 women and 12 men are selected randomly, what is the probability that the mean of the women will be more than 1.5 points higher than the mean of the men?
Explanation / Answer
here let A =Xbar -Ybar ; wher Xbar and Y bar are mean for 12 women and men
expected mean of A =E(Xbar)-E(Ybar)=3-2 =1
and std deviation of A =sqrt(1.52/12+1.52/12) =0.612
probability that the mean of the women will be more than 1.5 points higher than the mean of the men:
for normal distribution z score =(X-)/ here mean= = 1 std deviation == 2.121