The data suggests than one plausible model, for X, the number of named storms during hurricane season in a year, is a population distribution having mean $\mu$ and standard deviation $\sigma$. If the standard deviation for a random sample of size 85 is 1.5, what is the standard deviation for a random sample of size 340?
A) 0.38
B) 6.00
C) 0.75
D) 1.50

Question

The data suggests than one plausible model, for X, the number of named storms during hurricane season in a year, is a population distribution having mean $\mu$  and standard deviation $\sigma$. If the standard deviation for a random sample of size 85 is 1.5, what is the standard deviation for a random sample of size 340?
A) 0.38
B) 6.00
C) 0.75
D) 1.50

Quizplus · Accepted Answer

The standard deviation of a sample is inversely proportional to the square root of the sample size. Therefore, if the sample size increases from 85 to 340 (which is 4 times larger), the standard deviation will decrease by a factor of 2 (the square root of 4). Thus, the new standard deviation is 1.5 / 2 = 0.75.

The Data Suggests Than One Plausible Model, for X, the Number