A sample of 26 elements from a normally distributed population is selected. The sample mean is 10 with a standard deviation of 4. The 95% confidence interval for $\mu$ is
A)6.000 to 14.000
B)9.846 to 10.154
C)8.384 to 11.616
D)8.462 to 11.538

Question

Quizplus · Accepted Answer

The 95% confidence interval for the mean is calculated using the formula: $\bar{x} \pm t_{\alpha/2} \times \frac{s}{\sqrt{n}}$. With 25 degrees of freedom, the t-value is approximately 2.060. Thus, the interval is $10 \pm 2.060 \times \frac{4}{\sqrt{26}}$, which is approximately 8.384 to 11.616.

A Sample of 26 Elements from a Normally Distributed Population μ\muμ

A Sample of 26 Elements from a Normally Distributed Population $\mu$