Question

An inspector inspects large truckloads of potatoes to determine the proportion p in the shipment with major defects prior to using the potatoes to make potato chips. Unless there is clear evidence that this proportion p is less than 0.10, he will reject the shipment. He will test the hypotheses H0: p = 0.10, Ha: p < 0.10. He selects an SRS of 200 potatoes from the more than 5000 potatoes on the truck. Suppose that 12 of the potatoes sampled are found to have major defects. The P-value of this test is:

Answer 1

Answer:

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

Replacing the info given we got:

$z=\frac{0.06-0.10}{\sqrt{\frac{0.10(1-0.10)}{200}}}=-1.89$  

And the p value would be given by:

$p_v =P(z$  

Step-by-step explanation:

Information given

n=200 represent the random sample taken

X=12 represent the potatoes with major defects

$\hat p=\frac{12}{200}=0.06$ estimated proportion of potatoes with major defects

$p_o=0.10$ is the value that we want to test

z would represent the statistic

$p_v$ represent the p value

Hypothesis to test

We want to check if the true proportion is less than 0.10 so then the system of hypothesis are:  

Null hypothesis:$p\geq 0.1$  

Alternative hypothesis:$p < 0.10$  

The statistic is given by:

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

Replacing the info given we got:

$z=\frac{0.06-0.10}{\sqrt{\frac{0.10(1-0.10)}{200}}}=-1.89$  

And the p value would be given by:

$p_v =P(z$