Question

Use the standard normal distribution or the t-distribution to construct a 90% confidenceinterval for the population mean. Justify your decision. If neither distribution can be used,explain why. Interpret the results.In a random sample of 50 people, the mean body mass index (BMI) was 26.9 and thestandard deviation was 6.06.O B. Neither distribution can be used to construct the confidence interval.Interpret the results. Choose the correct answer below.O A. If a large sample of people are taken approximately 90% of them will have aBMI between the bounds of the confidence interval.OB. It can be said that 90% of people have a mi between the bounds of theconfidence intervalO C. With 90% confidence, it can be said that the population mean BMI is betweenthe bounds of the confidence interval.OD. Neither distribution can be used to construct the confidence interval.PS

Answer 1

A confidence interval, in statistics, refers to the probability that a population parameter will fall between a set of values for a certain proportion of times.

Strictly speaking a 90% confidence interval means that if we were to take 100 different samples and compute a 90% confidence interval for each sample, then approximately 90 of the 100 confidence intervals will contain the true mean value (μ).

Comparing these statements to the options, we can say that

The correct answer is option C. Because it reflects the definition of Confidence interval