Question

We must have a random sample when investigating the confidence interval of µ.

I am confused by this question. Is this true or false and why.

Answer 1

It is true , as we know we need sample to calculate confidence interval µ, nowhere is a question why we need randomness , here randomness means every entity in population have the same probability of being chosen in sample suppose we have a data that is height of 200 people now every one of 200 people have equal probability that they are chosen in a sample to represent population , basically sample is representative of population and it should represent population unbiasedly , suppose in our data of 200 people of height we take a sample of 20 people not randomly we assign higher probability to tall people for being selected in sample , so now in our sample there are more tall people , now when we calculate mean of our sample , it is more deviated from the population because it represent most of the tall people in sample , and when we will take confidence interval of population mean , it will not correctly represent the confidence of the population mean to be in the confidence interval range