Answer:
[tex] n = (\frac{2.326*1.7}{0.3})^2= 173.73[/tex]
And the value for n rounded up would be n = 174
Step-by-step explanation:
We have the following info given:
[tex] s= 1.7[/tex] previous estimation for the deviation
[tex] ME=0.03[/tex] the margin of error desired
[tex] Conf =0.98[/tex] represent the confidence
The Margin of error is given by:
[tex] ME = z_{\alpha/2} \frac{\sigma}{\sqrt{n}}[/tex]
If we solve for the value of n we got:
[tex] n= (\frac{z*\sigma}{ME})^2[/tex]
For this problem we know that the confidence is 98% so then the significance level would be [tex]\alpha=0.02[/tex] and the critical value would be:
[tex] z_{\alpha/2}= 2.326[/tex]
And replacing we got:
[tex] n = (\frac{2.326*1.7}{0.3})^2= 173.73[/tex]
And the value for n rounded up would be n = 174
