Question

Researchers working the mean weight of a random sample of 800 carry-on bags to e the airline. Which of the following best describes the effect on the bias and the variance of the estimator if the researchers increase the sample size to 1,300?

(A) The bias will decrease and the variance will remain the same.
(B) The bias will increase and the variance will remain the same.
(C) The bias will remain the same and the variance will decrease.
(D) The bias will remain the same and the variance will increase.
(E) The bias will decrease and the variance will decrease.

Answer 1

(E) The bias will decrease and the variance will decrease.

Explanation:

Given that researchers working the mean weight of a random sample of 800 carry-on bags to e the airline.

We have to find out the effect of increasing the sample size on variance and bias.

We know as per central limit theorem, sample mean follows a normal distribution with mean = sample mean

and std deviation of sample mean = std error =
`(std dev)/(√(n) )`

Thus std error the square root of variance is inversely proportional to the square root of sample size.

Also whenever we increase sample size the chances of bias would decrease as the sample size becomes larger

So correct answer is both bias and variation will decrease.

(E) The bias will decrease and the variance will decrease.