A semiconductor firm produces logic devices. The contract with their customer calls for a fraction defective of no more than 0.02. A random sample of 190 devices yields a total of 37 defectives. What is the value of the test statistic for the appropriate hypothesis test

We are given that a semiconductor firm produces logic devices. The contract with their customer calls for a fraction defective of no more than 0.02. A random sample of 190 devices yields a total of 37 defectives.

Let p = proportion of defective devices

Let Null Hypothesis, [tex]H_0[/tex] : p [tex]\leq[/tex] 0.02 {means that fraction defective is no more than 0.02}

Alternate Hypothesis, [tex]H_a[/tex] : p > 0.02 {means that fraction defective is more than 0.02}

The test statistics that will be used here is One-Sample proportion test;

T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)

where, [tex]\hat p[/tex] = proportion of defectives in a sample of 190 = [tex]\frac{37}{190}[/tex]

n = sample of devices = 190

So, test statistics = [tex]\frac{\frac{37}{190} -0.02}{\sqrt{\frac {\frac{37}{190}(1-\frac{37}{190})}{190} } }[/tex]

= 6.082

Therefore, the value of the test statistic for the appropriate hypothesis test is 6.082.