Question

A student organization plans to ask 100 randomly selected students how much they spent on textbooks last semester. You argue for a sample of 900 students instead of 100. You know that the standard deviation of the sample mean x of the amounts spent will be _____ times as large with the larger sample. What should the blank "_____" be:1) three2) one-ninth3) one-third4) nine

Answer 1

3) one-third

Explanation:

the proportion between the standard deviations is

`(s2)/(s1)` =
`\sqrt{(N1)/(N2) }` where

• s1,s2 are the standard deviations of the samples 1 and 2
• N1,N2 are the sample sizes of the samples 1 and 2.

If sample 1 is the sample with 100 students and sample 2 is the sample with 900 students, then

`(s2)/(s1)` =
`\sqrt{(100)/(900) }` =
`(1)/(3)`

Therefore,

the standard deviation of the sample mean x of the amounts spent will be one-third times as large with the larger sample