Statistical Tables and Charts Find the probability of type I error if exactly 60

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Statistical Tables and Charts

Find the probability of type I error if exactly 60% of the voters favor the use of these fuels.

the absolute tolerance is +/-0.0003

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What is the type II error probability ? if 75% of the voters favor this action?

A random sample of 500 registered voters in Phoenix is asked if they favor the use of oxygenated fuels year-round to reduce air pollution. If more than 314 voters respond positively, we will conclude that at least 60% of the voters favor the use of these fuels.

Round your answers to four decimal places (e.g. 98.7654).

Statistical Tables and Charts

Explanation / Answer

Solution:

(a) 314/500 = 0.628
SE = sqrt(pq/n) = sqrt(0.6*0.4/500) = 0.022
Z = (sample-mean)/SE = (0.628-0.6)/0.022 = 1.27
P(Z > 1.27) = 1?P (Z < 1.27)
= 1?0.898 = 0.102

(b) SE = sqrt(0.75*0.25)/500) = 0.0193
Z = (0.628-0.75)/0.0193 = 2.70
P(Z < -6.32) = 1?P (Z < 6.32) = 1?1 = 0

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