Advanced Micro Devices (AMD) makes controllers for toy cars. New Bright Industri

Question

Advanced Micro Devices (AMD) makes controllers for toy cars. New Bright Industrial Company, a firm that manufactures toy cars, requires each batch of controllers sent by AMD to have a defect rate that doesn’t exceed .05. (That is, the proportion of defective controllers in each batch shipped must be .05 or less.) Assume New Bright tests a batch of 200 controllers, and that 4 controllers are found to be defective.

Assume the null hypothesis is p = .05 and the alternate hypothesis is p < .05. Assume the statistic used to test the hypothesis is the sample proportion, and that the significance level chosen is .05. Assume further that the true mean is .03. Calculate the probability of making a Type II error.

Explanation / Answer

for P =0.05 and Po =0.03 ; n=200

here at 0.05 level of signifcance critical value z= -1.645

therefore critical value for not rejecting null hypothesis: phat =P +z*std error =0.05-1.645*(P(1-P)/n)1/2

0.05-1.645*0.0154 =0.02465

std error for true proportion =(P0*(1-P0)/n)1/2 =0.0121

therefore type II error =P(P>0.02465) =P(Z>(0.02465-0.03)/0.0121)=P(Z>-0.4434)=0.6713

please revert for any clarification required

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