STATISTICS - HYPOTHESIS TESTING
A village council has to decide whether or not to build a new village hall. In one road of the village, out of 120 residents, 54 thing the new hall would be a waste of money. Working at the 5% sig level, test the hypothesis that the villagers are evenly divided for and against the new building.
In the answers it says:
Let p=proportion in favour

H0: P=0.5
H1: P

Question

STATISTICS - HYPOTHESIS TESTING
A village council has to decide whether or not to build a new village hall. In one road of the village, out of 120 residents, 54 thing the new hall would be a waste of money. Working at the 5% sig level, test the hypothesis that the villagers are evenly divided for and against the new building.
In the answers it says:
Let p=proportion in favour

H0: P=0.5
H1: P<0.5

Why is H1: P<0.5? To me it would make more sense to have H1 as P≠0.5.

anonymous · Answer

Let p=proportion in favour

H0: P=0.5
H1: P<0.5

Why is H1: P<0.5? To me it would make more sense to have H1 as P≠0.5.

anonymous · Answer

is the hint!

anonymous · Answer

Yes but why is hypothesis 1 P<0.5? Nowhere in the question does it mention less than, so surely it would be better to test whether the proportion is equal or not equal?

ash2326 · Answer

If H1 $\ne0.5$ this can be anything H1 can also be 0.8 but we want it to be less than 0.5 cause then only it'll indicate the proportion in favor less than half

anonymous · Answer

Why only take into account less than half, why not more than half as well?