Statistics: A recent study of 40 randomly selected children ages 6-8 found that the mean length of time spent watching television

Question

A recent study of 40 randomly selected children ages 6-8 found that the mean length of time spent watching television each week was 12 hours and the standard deviation was 2.5 hours. The mean time 35 randomly selected children ages 9-11 spent watching television each week was 13 hours and the standard deviation was 2.8 hours. Construct a 95% confidence interval for μ1 - μ2.

 

 

 

A.(-2.001, -1.873)
B.(-1.968, 1.561)
C.(-1.673, 1.892)
D.(-2.209, 0.209)

Answer 1

There is only one correct choice for the mean of 12-13 = -1 and that is choice D.

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If the poser of the question has made it tougher, he might have made sure that all the confidence intervals centered on -1, but had different sizes, then you would have had to calculate the 95% confidence interval more accurately.

 

To do so, you would need to calculate the standard error for each mean value and then calculate the standard error for the difference which would have been the square root of the sum of each of the errors squared (=0.617).  Then the 95% confidence interval would have to be 3.92 times this value (=2.4172) centered around -1.