Respuesta :
Answer:
[tex]n=\frac{0.0875(1-0.0875)}{(\frac{0.02}{1.96})^2}=766.82[/tex]
And rounded up we have that n=767
Step-by-step explanation:
We know the following info:
[tex] n=160[/tex] represent the sample size selected
[tex] x= 14[/tex] represent the number of defectives in the sample
[tex]\hat p= \frac{14}{160}= 0.0875[/tex] represent the estimated proportion of defectives
[tex] ME = 0.02[/tex] represent the margin of error desired
The margin of error for the proportion interval is given by this formula:
[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex] (a)
And on this case we have that [tex]ME =\pm 0.02[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex] (b)
The crtical value for a confidence level of 95% is [tex] z_{\alpha/2}=1.96[/tex]
And replacing into equation (b) the values from part a we got:
[tex]n=\frac{0.0875(1-0.0875)}{(\frac{0.02}{1.96})^2}=766.82[/tex]
And rounded up we have that n=767
