The lower and upper limits of the 68.26% confidence interval for the population mean $\mu$ , given that n = 64, $\bar { x }$ = 110 and $\sigma$ = 8, are 109 and 111, respectively.

Question

Quizplus · Accepted Answer

The formula for a 68.26% confidence interval is:

$$\bar{x} \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$$

where $\alpha$ = 1 - 0.6826 = 0.3174 and $z_{\alpha/2}$ is the z-score for the upper tail probability of 0.1587.

From the standard normal distribution table, we find that $z_{\alpha/2}$ = 0.9945.

Substituting the given values, we get:

$$\bar{x} \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}} = 110 \pm 0.9945\frac{8}{\sqrt{64}} = (109, 111)$$

Therefore, the statement is true.

The Lower and Upper Limits of the 68 μ\muμ , Given That N = 64

The Lower and Upper Limits of the 68 $\mu$ , Given That N = 64