I was doing a few practice problems regarding Null Hypothesis Testing and I got this question wrong:
Rains asks his students to test the null hypothesis that states for every new well drilled, profits will be increased by the given multiple of the coefficient, all other factors remaining constant. The appropriate hypotheses for this two-tailed test can best be stated as:
The correct answer is:
H0: b1 = 0.98 versus Ha: b1 ≠ 0.98.
I got confused because I thought, the null hypothesis is what you want to reject. If you want to prove that b1=0.98, shouldn´t the null hypothesis be:
Ho: b1≠ 0.98 versus Ha: b1=0.98 ??
The answer explanation from Kaplan is:
The coefficient given in the above table for the number of new wells drilled (WLS) is 0.98. The hypothesis should test to see whether the coefficient is indeed equal to 0.98 or is equal to some other value. Note that hypotheses with the “greater than” or “less than” symbol are used with one-tailed tests.
The null hypothesis _ always _ includes the equal sign, irrespective of what you think you want to reject. Hₒ cannot be b1 ≠ 0.98.
You are correct the null is what your are trying to reject. Think of the null as the worst case scenario. But as S2000 said the null must equal something.
For example we may want to test whether the true value of the wells is different to 0.98 then we set the null here to 0.98. (We want to reject this)
The Alt becomes Not equal to 0.98 (what we are hoping for)
Compute the T stat (observed value - hypothesized / SE), compare it to the T table and if the computed T Is greater than the TC we reject this assumption and assume that the result of the well drill IS different to 0.98. (We do not say we accept the alternative, we simply say we reject the null or fail to reject the null) In other words we are happy to see this is different to 0.98 as it means our test is statistically significant and confirms our observations
Thanks Rex for the explanation.