Question

A bootstrap sampling distribution was constructed for a single mean. The sample mean was 100 and the standard deviation was 15. Given a sample size of 30 the standard error was 2.739. If the sample size were increased to 500, how would the standard error change?

a. It would increase.
b. It would stay the same.
c. It would decrease.

Answer 1

Increasing the sample size from 30 to 500 would decrease the standard error because the formula for standard error involves dividing the standard deviation by the square root of the sample size, and as the denominator increases, the standard error decreases.

Step-by-step explanation:

The question is about the change in standard error when the sample size in bootstrap sampling distribution is increased. Given that the original sample size is 30 with a standard deviation of 15 and a sample mean of 100, resulting in a standard error of 2.739, we need to determine the effect of increasing the sample size to 500 on the standard error.

The standard error of a sample mean is calculated using the formula SE = s / √n, where s represents the standard deviation of the sample and n the sample size. As the sample size increases, the denominator of this formula (√n) increases, which in turn decreases the standard error since the same standard deviation is being divided by a larger number. Thus, if we increase the sample size from 30 to 500, the standard error would decrease.

So, the correct answer to the question is:
c. It would decrease.

Answer 2

c. It would decrease

Step-by-step explanation:

When you increase the sample size, you decrease the standard/marginal error since you have a bigger representation of the population. However, this would take time and money to collect data for these big samples.