AP® Statistics

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You're Applying to How Many Colleges? A Test


Conventional wisdom says that high school seniors should apply to about $6$ – $8$ colleges. Some sources recommend applying to as many as $10$ colleges. Talia thinks that the actual average number of colleges that seniors at her school have applied to this year is greater than $10$, so she decides to do a study and perform a one-sample $t$-test for the population mean.

The results of Talia's test will not be reliable if which of the following is found to be true?


The distribution of the number of colleges applied to by seniors at her school this year is found to be approximately normal.


Talia randomly selects seniors at her school to survey for her study.


Those seniors who Talia surveyed all provide truthful responses about the number of colleges they applied to.


Talia does not know the standard deviation for the number of colleges applied to by all seniors at her school.


Talia uses a sample size of $20$ and finds that the sample contains a few very high outliers.