Choose the one alternative that best completes the statement or answers the question.
-In a sample of 10 randomly selected employees, it was found that their mean height was $63.4$ inches. From previous studies, it is assumed that the standard deviation, $\sigma$, is $2.4$. Compute the $95 \%$ confidence interval for $\mu .$
A) $( 61.9,64.9 )$
B) $( 58.1,67.3 )$
C) $( 59.7,66.5 )$
D) $( 60.8,65.4 )$

Question

Quizplus · Accepted Answer

To compute the 95% confidence interval for the population mean $\mu$, we use the formula: $\bar{x} \pm Z \frac{\sigma}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $Z$ is the Z-score corresponding to the desired confidence level (for 95%, $Z = 1.96$), $\sigma$ is the population standard deviation, and $n$ is the sample size. Plugging in the given values: $63.4 \pm 1.96 \frac{2.4}{\sqrt{10}}$ gives the interval $(61.9, 64.9)$.

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