Cholesterol levels are measured on a random sample of 1,000 persons, and the sample standard deviation is calculated. Suppose a second survey were repeated in the same population, but the sample size tripled to 3,000. Then which of the following is true?

a. The new sample standard deviation would tend to be smaller than the first and approximately about one-third the size.
b. The new sample standard deviation would tend to be larger than the first and approximately about three times the size.
c. The new sample standard deviation would tend to be larger than the first, but we cannot approximate by how much.
d. None of the above is true because there is no reason to believe one sample standard deviation would tend to be systematically larger