Assume that you wish to estimate a population proportion, p. For the given margin of error and confidence level,determine the sample size required.
-You wish to estimate the proportion of shoppers that use credit cards. Obtain a sample size that will ensure a margin of error of at most 0.01 for a 95% confidence interval. It is deemed reasonable
To presume that of those sampled, the percentage using credit cards will be at least 56%.

Question

Quizplus · Accepted Answer

To determine the sample size required for estimating a population proportion with a specific margin of error and confidence level, we use the formula: $n = \frac{Z^2 \times p(1-p)}{E^2}$, where $Z$ is the Z-score corresponding to the confidence level, $p$ is the estimated proportion, and $E$ is the margin of error. For a 95% confidence interval, the Z-score is approximately 1.96. Given that $p = 0.56$ and $E = 0.01$, we substitute these values into the formula: $n = \frac{(1.96)^2 \times 0.56(1-0.56)}{(0.01)^2}$, which calculates to approximately 9466, rounding to the nearest whole number.

Assume That You Wish to Estimate a Population Proportion, P