Question

Researchers working for a certain airline are investigating the weight of carry-on bags. The researchers will use the mean weight of a random sample of 1,300 carry-on bags to estimate the mean weight of all carry-on bags for 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 800?

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

Answer:

d. The bias will remain the same and the variance will increase.

Step-by-step explanation:

Sample size and bias:

800 is still a large sample size, so the bias will remain the same.

Variance:

From a data set of size n with mean M, the variance is given by:

$V = \sum_{i=0}^{n} \frac{(x_i - M)^2}{n}$

So as we decrease the sample size, variance increases.

So the correct answer is given by option d.

Answer 2

They do have the following relation for a random selection of n elements from a population with a mean of p and variation $\sigma^2$.

         $\to \mathbb{E} (\bar{x}) = \mu;\\\\\to Var(\bar{x}) = \frac{\sigma^2}{n}$    (where $\bar{x}$ is the sample mean)

• As a result, $\bar{x}$ is an impartial estimate of the population mean.
• As a result, bias remains 0 and is influenced by sample size changes.
• Its estimator's variance, on the other hand, is inversely proportional to n and hence reduces as sample size increases.

Therefore, the answer is "Option C".

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