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
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.

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 $$\displaystyle{\left({30.7365},{36.2635}\right)}.$$