Question

A chip manufacturer tests the microprocessors produced from the production line process. The company made a statement (claim) that only 4% of its microprocessor production was damaged. To test whether the claim is true, a study was conducted by taking a sample of 577 microprocessors, of which 37 were damaged. Can the statement (claim) be rejected or accepted with a 99% confidence level?

Answer 1

$Let\;\hat p=\frac{37}{577}=0.064, p_{0}=0.04,n=577\\ a) H_{0}: p \geq 0.04\\ H_{1}: p < 0.04\\ Z_{α}=Z_{0.01}=2.326,\\ Z=\frac{\hat p -p_{0}}{\sqrt{\frac{ p_{0}(1-p_{0})}{n}}}\\ =\frac{0.064 -0.04}{\sqrt{\frac{0.04(0.96)}{577}}}=2.94\\ \text{the rejection region} :\; Z<-2.326\\ \text{The decision is to accept}:\; H_0\\ \text {This mean that the actual }\\ \text{percentage is more than or equals 0.04. }\\$