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 6.3. You want your sample mean & to estimate u with an error of no more than 1.3 point in either direction. (a) What standard deviation must have so that 99.7% of all samples give an x within 1.3 point of u? Use the 68-95-99.7 rule. (Enter your answer rounded to four decimal places.) standard deviation of x = (b) How large an SRS do you need in order to reduce the standard deviation of x to the value you found? (Enter your answer rounded to the nearest whole number) SRS size = Question Source Moore, The Basic Practice of Statistics, Be Publisher: W.H. Freeman Dell

Answer 1

Given o = 6.3. We want our sample mean x to estimate u with an error of no more than 1.3 point in either direction. a) According to the 68-95-99.7 rule we have Pr(u – 3s < x <+ 3s) = 0.9973 where s is the standard deviation required to be found. We are also given H – 3s = Ã – 1.3 and u + 3s = Ã + 1.3 So subtracting we get u +3s – (u – 3s) = (č + 1.3) - (8 – 1.3 ) or, 6s = 2.6

2.6 - S= 0.433 6 Thus standard deviation of i = 0.433 b) We are given that o = 6.3 and s = 0.433. Suppose the SRS size is n. Then s = n 6.3 6.3 or, 0.433 = or, vn 14.549 0.433 or, n = 211.67 212

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