Question

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

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