A sample of size $n = 20$ is drawn from an approximately normal population whose standard deviation is $\sigma = 5.5$. The sample mean is $\bar { x } = 52.4$. Construct a $95 \%$ confidence interval for $\mu$.
A) $35.69

Question

A sample of size $n = 20$ is drawn from an approximately normal population whose standard deviation is $\sigma = 5.5$. The sample mean is $\bar { x } = 52.4$. Construct a $95 \%$ confidence interval for $\mu$.
A) $35.69 < \mu < 69.11$
B) $49.99 < \mu < 54.81$
C) $52.40 < \mu < 54.81$
D) $51.37 < \mu < 53.43$

Quizplus · Accepted Answer

To construct a 95% confidence interval for the population mean $\mu$ when the population standard deviation $\sigma$ is known and the sample size $n$ is given, 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: $52.4 \pm 1.96 \frac{5.5}{\sqrt{20}}$, we get the interval $49.99 < \mu < 54.81$.

A Sample of Size n=20n = 20n=20 Is Drawn from an Approximately Normal Population Whose Standard Deviation

A Sample of Size $n = 20$ Is Drawn from an Approximately Normal Population Whose Standard Deviation