A marketing team wants to conduct a survey to estimate the proportion of customers who are satisfied with their new product. They want to achieve a 95% confidence level with a margin of error of no more than 3%. According to their preliminary research, they estimate that the proportion of satisfied customers is around 60%. What is the minimum sample size required for this survey? How will this answer change if the permissible margin of error is enhanced to 4%? Justify your answer.
Added by Shashi S.
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The formula to calculate the minimum sample size \( n \) needed to estimate a population proportion with a given margin of error \( E \) at a certain confidence level is: \[ n = \left(\frac{Z^2 \times p \times (1-p)}{E^2}\right) \] where: - \( Z \) is the Z-score Show more…
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