Hypothesis Testing Problem

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!

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.

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

You’re welcome.