Respuesta :
Testing the hypothesis, we have that since the p-value of the test is 0 < 1, our response is that the presumption underestimates the proportion of defective parts.
At the null hypothesis, we test if the proportion of defectives is of at most 1%, that is:
[tex]H_0: p \leq 0.01[/tex]
At the alternative hypothesis, we test if the proportion of defectives is of more than 1%, that is:
[tex]H_1: p > 0.01[/tex]
The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
From the sample, we have that:
[tex]n = 500, \overline{p} = \frac{15}{500} = 0.03[/tex]
Thus, the value of the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.03 - 0.01}{\sqrt{\frac{0.01(0.99)}{500}}}[/tex]
[tex]z = 4.49[/tex]
The p-value of the test is the probability of finding a sample proportion above 3%, which is 1 subtracted by the p-value of z = 4.49.
z = 4.49 has a p-value of 1.
1 - 1 = 0.
The p-value of the test is 0 < 1, which means that our response is that the presumption underestimates the proportion of defective parts.
A similar problem is given at https://brainly.com/question/24912812
