To estimate the mean score of those who took the Medical College Admission Test

Question

To estimate the mean score of those who took the Medical College Admission Test on your campus, you will obtain the scores of an SRS of students. From published information you know that the scores are approximately Normal with standard deviation about 6.5. You want your sample mean x¯ to estimate with an error of no more than 1.2 point in either direction

a. What standard deviation (±±0.0001) must x¯ have so that 99.7% of all samples give an x¯ within 1.2 point of ?

b. How large an SRS do you need in order to reduce the standard deviation of x¯ to the value you found in part (a)?

Explanation / Answer

Solution:-

a) such that P( - 3 < x < + 3 ) = 0.9973
By the question 3 must be equal to 1.2 for all samples.
so 3 = 1.2
= > = 1.2/3 = 0.4000

b)    since std=6.5/sqrt(n)=0.4

n = (6.5/0.4)^2 = 264.0625 = 265

(or)

==> 3 = 1.2/(6.5/sqrt(n))

n = ((3*6.5)/1.2)2 = (16.25)^2 = 264.0625 = 265 (rounded)

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