Question

Given sample informatio: displaystyleoverline{{{x}}}={34},sigma={4},{n}={10} to calculate the following confidence intervals for displaystylemu assuming the sample is from a normal population. 99 percent confidence. (Round your answers to 4 decimal places.)

Confidence intervals
ANSWERED
asked 2021-02-25
Given sample informatio: \(\displaystyle\overline{{{x}}}={34},\sigma={4},{n}={10}\) to calculate the following confidence intervals for \(\displaystyle\mu\) assuming the sample is from a normal population.
99 percent confidence. (Round your answers to 4 decimal places.)

Answers (1)

2021-02-26

Step 1
Solution:
Given that,
Sample size \(\displaystyle{n}={10}\)
Sample mean \(\displaystyle\overline{{{x}}}={34}\)
Population standard deviation \(\displaystyle\sigma={4}\)
Step 2
99 percent confidence interval:
Critical value:
The z-critical value at \(99\%\) confidence level is 2.58.
Margin of error:
The margin of error is calculated as given below:
\(\displaystyle{E}={z}_{{c}}{\left(\frac{\sigma}{\sqrt{{n}}}\right)}\)
\(\displaystyle={2.58}{\left(\frac{4}{\sqrt{{10}}}\right)}\)
\(\displaystyle={3.2635}\)
Calculation:
The \(99\%\) confidence interval for population mean can be calculated as follows:
\(\displaystyle{C}{I}=\overline{{x}}\pm{E}\)
\(\displaystyle={34}\pm{3.2635}\)
\(\displaystyle={\left({30.7365},{36.2635}\right)}\)
Hence, the \(99\%\) confidence interval for population mean is \(\displaystyle{\left({30.7365},{36.2635}\right)}.\)

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