Hypothesis Testing Problem

CFA Level I Quant
#1

Hi there!

I have a problem with stating the right Hypothesis Test for the following problem (chi-squared test):

“A study was conducted to determine whether the standard deviation of monthly maintenance costs of a Pepper III aircraft is $300.”

The correct statement is:

  • H0: pop. variance = 300^2
  • Ha: pop. variance =/ 300^2

However, when I read the problem, I was sure that Ha: pop. variance = 300^2. The solution says that the wording is a little tricky, but it does not explain how I am supposed to interpret it… Could you guys explain me the right way to interpret the wording of the problem? Thank you so much!

#2

The null hypothesis always includes the equal sign; the alternative hypothesis does not. If you’re testing whether the standard deviation of something is equal to a given value, then H0 is σ = k and Ha is σ ≠ k.

#3

Of course! I didn’t think about that! Thanks s2000magician

#4

You’re welcome.