Question

Find the P-value for the indicated hypothesis test. A manufacturer claims that fewer than 6% of its fax machines are defective. In a random sample of 97 such fax machines, 5% are defective. Find the P-value for a test of the manufacturer's claim. Group of answer choices 0.1736 0.1591 0.3264 0.3409

Answer 1

Answer:

$z=\frac{0.05 -0.06}{\sqrt{\frac{0.06(1-0.06)}{97}}}=-0.41471$  

The p value for this case would be given by this probability:

$p_v =P(z<-0.41471)=0.340$  

And the best answer would be:

0.3409

Step-by-step explanation:

Information given

n=97 represent the random sample taken

$\hat p=0.05$ estimated proportion of defective

$p_o=0.06$ is the value to verify

z would represent the statistic

$p_v$ represent the p value

Hypothesis to test

We want to verify if the true proportion of defectives is less than 0.06, the system of hypothesis are.:  

Null hypothesis:$p\geq 0.06$  

Alternative hypothesis:$p < 0.06$  

The statistic is:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)  

Replacing the info given we got:

$z=\frac{0.05 -0.06}{\sqrt{\frac{0.06(1-0.06)}{97}}}=-0.41471$  

The p value for this case would be given by this probability:

$p_v =P(z<-0.41471)=0.340$  

And the best answer would be:

0.3409