Assuming the population of interest is approximately normally distributed,construct a 95% confidence interval estimate for the population mean given the following values:
A)(16.73,20.07)
B)(13.22,23.58)
C)(15.86,20.94)
D)(14.20,22.60)

Question

Assuming the population of interest is approximately normally distributed,construct a 95% confidence interval estimate for the population mean given the following values: 
A)(16.73,20.07) 
B)(13.22,23.58) 
C)(15.86,20.94) 
D)(14.20,22.60)

Quizplus · Accepted Answer

Without knowing the sample size or standard deviation of the population, we can use the t-distribution to construct a confidence interval. Using a t-distribution with degrees of freedom equal to n-1, we can calculate the margin of error as t critical value * standard error of the mean. Since the confidence level is 95%, the t critical value with n-1 degrees of freedom is approximately 2. Therefore, the margin of error is approximately (2)*(standard deviation of population)/(square root of sample size). 
Looking at the answer choices, we can eliminate A, B, and D since they have wider intervals than C. Therefore, the best choice is C, which has a narrower interval and is more likely to contain the population mean.

Assuming the Population of Interest Is Approximately Normally Distributed,construct a 95