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loris [4]
3 years ago
7

You have been assigned to determine whether more people prefer Coke or Pepsi. Assume that roughly half the population prefers Co

ke and half prefers Pepsi. How large a sample do you need to take to ensure that you can estimate, with 95% confidence, the proportion of people preferring Coke within 3% of the actual value? [Hint: proportion est. = 0.5] Round your answer to whole number
Mathematics
1 answer:
Alex Ar [27]3 years ago
3 0

Answer:

n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11  

And rounded up we have that n=1068

Step-by-step explanation:

For this case we have the following info given:

ME=0.03 the margin of error desired

Conf= 0.95 the level of confidence given

The margin of error for the proportion interval is given by this formula:  

ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}    (a)  

the critical value for 95% of confidence is z=1.96

We can use as estimator for the population of interest \hat p=0.5. And on this case we have that ME =\pm 0.03 and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}   (b)  

And replacing into equation (b) the values from part a we got:

n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11  

And rounded up we have that n=1068

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