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You're Applying to How Many Colleges? A Test

APSTAT-3BH1YL

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?

A

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

B

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

C

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

D

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

E

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