# Null hypothesis definition

In the Schweser answers to the comprehensive problems for the chapter on hypothesis testing, it states: “The null hypothesis is typically the one the researcher want to disprove.” It seems like that is wrong. In the CFA text, it is stated: “The null hypothesis is a proposition that is considered true unless the sample we use to consider the hypothesis test give convincing evidence that the null hypothesis is false.” Am I correct is disagreeing with the Schweser text?

They’re both correct. Suppose you are curious if red apples are larger than green ones. The Null hypothesis H_0 would be that red apples are not larger than green ones, and the alternative hypothesis H_A is that red apples are larger than green ones. To reject the null hypothesis, you must be reasonably assured that the average size of green apples is larger than the average size of red apples. The key is to know what is a significant result, or what is just noise due to normal variations you’d see in a small sample size.

So, am I correct in assuming that the null is what you are trying to prove false, but you can’t unless you can statistically reject it?

Yes, that is how I typically think about it.

Here is a question I got wrong while studying today: Austin Roberts wants to determine whether the mean price of houses in the area is greater than \$145,000. A random sample of 36 houses in the area has a mean price of \$149,750. The pop. standard deviation is \$24,000, and Roberts wants to conduct hypothesis testing at a 1 percent level of significance. I thought the null hyp. should have been: mean price is greater than or equal to \$145,000. But, it should have been: mean price in area is less than or equal to \$145,000, since he is trying to prove that statement false. Am I correct?

Typically in most statistical text books They would go and say “Reject the Null Hypothesis” and “Fail to reject the Null Hypothesis” for this very reason.

Yes, you are correct. Note the null hypothesis is p<= 145k, and alternative hypothesis is p>145k. Ie, alternative is NOT p>=145k.

cpk123 Wrote: ------------------------------------------------------- > Typically in most statistical text books > > They would go and say “Reject the Null > Hypothesis” > and > “Fail to reject the Null Hypothesis” > > for this very reason. Yes, more specifically, one does NOT accept the null hypothesis, one just fails to reject it. Subtle difference.

If you looked at it another way: What they try to prove in the question is the WORDING for your Alternate hypothesis. So Austin Roberts wants to determine whether the mean price of houses in the area is greater than \$145,000. A random sample of 36 houses in the area has a mean price of \$149,750. The pop. standard deviation is \$24,000, and Roberts wants to conduct hypothesis testing at a 1 percent level of significance. HA: mean > 145 Then H0: mean <= 145 would come naturally.