)The random sample shown below was selected from a normal distribution
Complete parts (a) and (b). Construct a 99% confidence interval for the population mean u.
Round to two decimal places as needed.
To construct a confidence interval for a population mean, we need to have the sample mean, sample standard deviation, sample size, and the level of confidence. Without the specific values of these parameters, it is not possible to calculate the confidence interval.
However, I can explain the general process of constructing a confidence interval for a population mean using a random sample:
(a) Calculate the sample mean (x̄) and sample standard deviation (s), assuming these values are provided in the question.
(b) Determine the critical value based on the level of confidence. For a 99% confidence level, the critical value can be found using a Z-table. The critical value for a 99% confidence level would typically be around 2.576.
(c) Calculate the margin of error using the following formula:
Margin of Error = (Critical Value) * (Standard Deviation of Sample / Square Root of Sample Size)
In this case, the standard deviation of the sample ('s') is used instead of the population standard deviation.
(d) Construct the confidence interval by subtracting and adding the margin of error to the sample mean:
Confidence Interval = Sample Mean ± Margin of Error
Remember to round the confidence interval to the desired number of decimal places as specified in the question.
For a more accurate and specific calculation, please provide the sample mean, sample standard deviation, sample size, and level of confidence.