Respuesta :
Answer:
[tex]n=(\frac{2.58(0.004)}{0.001})^2 =106.50 \approx 107[/tex]
So the answer for this case would be n=107 rounded up to the nearest integer
Step-by-step explanation:
Information given
[tex]\bar X= 0.996[/tex] the sample mean
[tex] s=0.004[/tex] the sample deviation
[tex] n =25[/tex] the sample size
Solution to the problem
The margin of error is given by this formula:
[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (a)
And on this case we have that ME =0.001 and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex] (b)
We can use as estimator of the real population deviation the sample deviation for this case [tex]\hat \sigma = s[/tex]/ The critical value for 99% of confidence interval is given by [tex]z_{\alpha/2}=2.58[/tex], replacing into formula (b) we got:
[tex]n=(\frac{2.58(0.004)}{0.001})^2 =106.50 \approx 107[/tex]
So the answer for this case would be n=107 rounded up to the nearest integer
