A 2014 survey asked 901 women and 775 men what they thought the ideal number of

Question

A 2014 survey asked 901 women and 775 men what they thought the ideal number of children for a family to have would be. The average number for women was 2.58 and the average number for men was 2.31. Assume that the population standard deviation for women is 0.8 and the population standard deviation for men is 0.88. Construct a 95% confidence interval for the difference in mean number of children for women and men. a. x bar 1-x bar 2= b. margin of error= c. lower and upper limit d. we are ___% confident that the true difference in population means is between ___ and ___

Explanation / Answer

n1 = 901 , x1 = 2.58 , s1 = 0.8

n2 = 775 , x2 = 2.31 , s2= 0.88

z value at 95% = 1.96

a)

xbar1 - xbar2 = 2.58 - 2.31 = 0.27

b)

margin of error= z * sqrt(s1^2/n1 + s2^2/n2)

= 1.96 * sqrt(0.8^2/901 + 0.88^2/775)

= 0.081

c)

CI = (x1 - x2) +/-   z * sqrt(s1^2/n1 + s2^2/n2)

= 0.27 + /- 0.081

= (0.189,0.351)

Lower limit = 0.189

Upper limit = 0.351

d)

we are 95 % confident that the true difference in population means is between 0.189 and 0.351

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