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

And rounded up we have that n=1068

Step-by-step explanation:

For this case we have the following info given:

the margin of error desired

the level of confidence given

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

   (a)  

the critical value for 95% of confidence is

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

  (b)  

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

And rounded up we have that n=1068