At one hospital, a random sample of 100 women giving birth to their first child is selected. Among this sample, the mean age was $25.6$ with a standard deviation of $5.9$. Find the $95 \%$ confidence interval. Round your answer to two decimal places.

Question

Quizplus · Accepted Answer

To find the 95% confidence interval for the mean age, we use the formula: $\bar{x} \pm z\frac{\sigma}{\sqrt{n}}$, where $\bar{x} = 25.6$, $\sigma = 5.9$, $n = 100$, and $z$ for a 95% confidence level is approximately $1.96$. Plugging these values in gives a margin of error of $1.16$, leading to a confidence interval of $24.44$ to $26.76$, which rounds to $24.42 < \mu < 26.78$.

At One Hospital, a Random Sample of 100 Women Giving 25.625.625.6

At One Hospital, a Random Sample of 100 Women Giving $25.6$