Question

A random sample of 55 measurements was selected from a population with standard deviation 10.3 and...

A random sample of 55 measurements was selected from a population with standard deviation 10.3 and unknown mean μ. Find a 99 % confidence interval for μ if the sample mean was 91.9

Homework Answers

Answer #1
One-Sample Z test Confidence Interval

We need to construct the 99% confidence interval for the population mean μ. We have been provided with the following information:
The sample mean is Xˉ=91.9, the population standard deviation is σ=10.3, the sample size is n=55, and the significance level is α=0.01

Critical Value
Based on the information provided, the significance level is α=0.01, therefore the critical value is Zc​=2.5758. This can be found by either using excel or the Z distribution table.

Margin of Error

The confidence interval:


Therefore, based on the data provided, the 99% confidence interval for the population mean is 88.3226<p<95.4774, which indicates that we are 99% confident that the true population mean μ is contained by the interval

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