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Margin of error: 0.04; confidence level: 95%; from a prior study, bold p with bold overparenthesis on top is estimated by the decimal equivalent of 89%. Find the sample size.

Respuesta :

JeanaShupp

Answer: 235

Step-by-step explanation:

The formula to calculate the sample size  :-

[tex]n=(\hat{p}(1-\hat{p}))(\dfrac{z_{\alpha/2}}{E})^2[/tex]

Given :  Estimated proportion [tex]\hat{p}=0.89[/tex]

Margin of error : [tex]E=0.04[/tex]

Significance level : [tex]\alpha=1-0.95=0.05[/tex]

Critical value : [tex]z_{\alpha/2} =1.96[/tex]

Now, the required sample size will be :-

[tex]n=(0.89(0.11))(\dfrac{(1.96)}{0.04})^2[/tex]

[tex]\Rightarrow\ n= 235.057\approx235[/tex]

Hence, the required minimum sample size = 235

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