Question

Discuss the importance of constructing confidence intervals for the population mean. What are confidence intervals? What is a point estimate? What is the best point estimate for the population mean? Explain. Why do we need confidence intervals?

Answer 1

Confidence Interval : The interval that can  be defined as the range of values with there specified probability of the values of the parameters lies within it

or

Confidence Interval can be defined as the range of values and can be derived from sample statistics that is likely to contain the values of an unknown population parameter

Confidence Interval can be used to bound the mean and standard deviation which can be obtain for regression coefficient and proportion and rates of occurence and also difference between population

Point Estimation : The estimation that can be defined as a single value that is used to estimate the population parameter

consider sample mean of X is a point estimate of the population mean $\mu$

-->Purposes of confidence intervals :

The interval that gives us a range of values within with certain probability with the true population value falls