Question

7. How large a sample we need to study BMI for young women to predict the Population Mean within ± 3 Margin of error at 80 % Confidence level, known ? ± 7.0?

Answer 1

Here we have given that

c=confidence level = 0.80

$\alpha$ =level of significance= 1-c=1-0.80=0.20

E=margin of error = 3

$\sigma$ = population standard deviation =7.0

Now we want to find the required sample size

we know the formula as follows

$n=(\frac{ Z \frac{\alpha}{2} *\sigma}{E})^2$

Now we find the Zcritical

Z c= $Z\frac{\alpha}{2}=Z\frac{0.20}{2}$ =Z (0.10) = 1.28 ( using Excel =NORMSINV(prob))

Now,

$n=(\frac{ Z \frac{\alpha}{2} *\sigma}{E})^2$

$=(\frac{ 1.28* 7.0}{3})^2$

=9

The Required sample size is 9

The 9 smaple we need to study BMI for young women to predict the population mean