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Catherine Chao, Director of Marketing Research, is evaluating consumer acceptance of a new toothpaste package. She plans to use a 95% confidence interval estimate of the proportion of households which prefer the new packages; she will accept a 0.05 error. Previous studies indicate that new packaging has an approximately 70% acceptance rate. The sample size should be at least _______.

Respuesta :

JeanaShupp

Answer: 323

Step-by-step explanation:

The formula to calculate the sample size for proportion is given by :_

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

Given : Significance level : [tex]\alpha: 1-0.95=0.095[/tex]

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

Margin of error : [tex]E=0.05[/tex]

The proportion of successes : [tex]p=0.70[/tex]

Now, the required sample size will be :-

[tex]n=0.70(0.30)(\dfrac{(1.96)}{0.05})^2=322.6944\approx323[/tex]

Hence, the minimum required sample size = 323

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