Question

Which is false?

A. A statistic is used to estimate an unknown parameter

B. Non sampling errors can be present even when a census is taken

C. Increase sample size to reduce bias

D. Margin of error will get smaller when you increase sample size

E. Variability describes how spread out the values of the sample statistic are when we take many samples.

Answer 1

a) A statistic is used to estimate the unknown population parameters.

Statistic is a function of sample values.

Hence this statement is TRUE.

b) Census is free from sampling errors but non sampling errors always occurs in census. Hence TRUE.

c) As sample size increases the sample carry more information about population.

Now I am little bit confused here that which bias is asked.

If, here you are asking about bias of the estimates of population parameters then definitely increase in sample size reduces the bias of the estimate and then statement is TRUE.

but, if you are asking about sample survey bias that is bias due to undercovarage or non response etc then these kind of bias can not be reduced even if you take a very large sample. Then this statement would be FALSE.

d) Margin of error is inversely proportional to the size of the sample.

Hence increase in sample size will give you a smaller margin of error. Hence this statement is TRUE.

e) For each sample the variability says about the measure of dispersion from the central values. Hence if we take many samples,

Variability describes how spread out the values of the sample statistic.