Question

Construct a 95% confidence interval to estimate the population mean using the following data. What assumptions need to be made to construct this​ interval?

x(over bar x)= 83   s=19    n=16

What assumptions need to be made to construct this​ interval?

A. The population is skewed to one side.

B. The sample size is less than 30.

C. The population mean will be in the confidence interval.

D. The population must be normally distributed.

With 95​% ​confidence, when n=16 the population mean is between the lower limit of _____ and the upper limit of _____

Answer 1

The correct option for assumptions needed to construct confidence interval is (D), i.e., The population must be normally distributed.

The confidence interval for population mean is calculated using the formula-

Given:

Critical value: For 95% confidence interval,

                                             

                                             

                                            

                                            

Lower limit : 72.8756125

Upper limit : 93.1243875

So, the 95% confidence interval for the population mean is (72.8756, 93.1244) Or .

Hence, the population mean is between the lower limit of 72.8756 and the upper limit of 93.1244