Question

# Another type of confidence interval is called a one-sided confidence interval. A one-sided confidence interval provides either a lower confidence boun

Confidence intervals

Another type of confidence interval is called a one-sided confidence interval. A one-sided confidence interval provides either a lower confidence bound or an upper confidence bound for the parameter in question. You are asked to examine one-sided confidence intervals. Presuming that the assumptions for a one-mean z-interval are satisfied, we have the following formulas for (1−α)-level confidence bounds for a population mean $$\displaystyle\mu$$: Lower confidence bound: $$\bar{x}-z_{\alpha} \cdot \sigma/\sqrt{n}$$, Upper confidence bound: $$\bar{x}+z_{\alpha} \cdot \sigma/\sqrt{n}$$. Interpret the preceding formulas for lower and upper confidence bounds in words.

We are $$(1-\alpha)100\%$$ confident that the mean of all individuals is higher than $$z_{\alpha} \text{(sample) standart deviations} \frac{\sigma}{\sqrt{n}} \text{below the sample mean}\ \overline{x}$$.
We are $$(1-\alpha)100\%$$ confident that the mean of all individuals is higher than $$z_{\alpha} \text{(sample) standart deviations} \frac{\sigma}{\sqrt{n}} \text{above the sample mean}\ \overline{x}$$.