Q 8.41 - Elementary Statistics

Question

Suppose that you have obtained data by taking a random sample from a population and that you intend to find a confidence interval for the population mean, $\mu$. Which confidence level, $95\%$ or $99\%$, will result in the confidence interval giving a more accurate estimate of $\mu$ ?

Step-by-Step Solution

Answer

Confidence level of $95\%$ will estimate population mean more precisely.

Step 1: Given Information

Data is obtained by taking a random sample from population. Two confidence intervals of value $95\%, 97\%$ are available to measure population mean.

Step 2: Explanation

As we know that larger confidence level results in larger confidence interval of $\mu$.

Hence, for $99\%$ confidence interval, we will obtain $\mu$ of smaller length as compared to that of $99\%$.

Therefore the estimation of population mean is better in case of $95\%$ as compared to $99\%$.