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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
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asked 2021-06-26

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.

Answers (1)

2021-06-27

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 \(z_{\alpha} \text{(sample) standart deviations} \frac{\sigma}{\sqrt{n}} \text{above the sample mean}\ \overline{x}\).

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asked 2020-11-07

Here are summary stastistics for randomly selected weights of newborn girls: \(\displaystyle{n}={224},\overline{{{x}}}={28.3}\text{hg},{s}={7.1}\text{hg}\). Construct a confidence interval estimate of mean. Use a 98% confidence level. Are these results very different from the confidence interval \(\displaystyle{26.5}\text{hg}{<}\mu{<}{30.7}\text{hg}\) with only 14 sample values, \(\displaystyle\overline{{{x}}}={28.6}\) hg, and \(\displaystyle{s}={2.9}\) hg? What is the confidence interval for the population mean \(\displaystyle\mu\)?

\(\ {27,2 \ hg<}\mu{<29,4 \ hg}?\) (Round to one decimal place as needed).

Are the results between the two confidence intervals very different?

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