Question

Given Data:

(1)= low lead level (2)= medium lead level, (3)= high lead level

IQ: 85 (1), 94 (1), 97 (1), 86 (1), 86 (1), 107 (1), 91 (1), 99 (1), 115 (1), 50 (1), 93 (1), 98 (1), 100 (1), 94 (1), 73 (1), 76 (1), 72 (1), 76 (1), 95 (1), 89 (1), 96 (1), 108 (1), 74 (1), 72 (2), 90 (2), 100 (2), 91 (2), 98 (2), 91 (2), 85 (2), 97 (2), 91 (2), 78 (2), 82 (3), 93 (3), 89 (3), 94 (3), 88 (3), 83 (3), 76 (3).

N=40 Mean=88.8 Standard deviation= 11.92

2a) For your sample of 40 IQ scores, find the IQ values that correspond to z-scores of 2.00 and -2.00, and use these calculations to determine if your sample contains any statistically significant IQ values (i.e. unusual values).

b) Using your sample statistics, calculate the 86th percentile of IQ scores for the population of children that live near the lead smelter. Draw a diagram to show your analysis of the problem.

Answer 1

n = 40

= 88.8

s = 11.92

A.

Z = (X-)/s

So, for z =

xl = 88.8 - 2*11.92

= 64.96

xu = 88.8 + 2*11.92

= 112.64

So the unusual values are: 50(1), 115(1)

B.

P(Z<z) = 0.86

So,

z = 1.08

(X-)/s = 1.08

x = 88.8 + 1.08*11.92

= 101.674

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