Question

A skeptical paranormal researcher claims that the proportion of Americans that have

seen a UFO, p, is less than 4 in every one thousand.Assuming that a hypothesis test is conducted to test this claim, identify the null hypothesis H0 and the alternative hypothesis Ha.
A. H0: p < 0.004
H1: p 0.004
B. H0: p > 0.004
H1: p 0.004
C. H0: p = 0.004
H1: p > 0.004
D. H0: p > 0.004
H1: p < 0.004

Answer 1

Null hypothesis:
`p \leq 0.004`

Alternative hypothesis:
`p >(4)/(1000)=0.004`

Alternatively we can express the system of hypothesis like this:

Null hypothesis:
`p = 0.004`

Alternative hypothesis:
`p >(4)/(1000)=0.004`

And the most reasonable choice for the options given it seems

C. H0: p = 0.004

H1: p > 0.004

Because in the null hypothesis we always need to have an equal sign and the optiosns A, B and D are not satisfying this condition

Explanation:

For this test we are trying to test the following claim "the proportion of Americans that have seen a UFO, p, is less than 4 in every one thousand" and that would represent the alternative hypothesis. And by the complement rule we will have the null hypothesis.

Based on this the system of hypothesis for this case are:

Null hypothesis:
`p \leq 0.004`

Alternative hypothesis:
`p >(4)/(1000)=0.004`

Alternatively we can express the system of hypothesis like this:

Null hypothesis:
`p = 0.004`

Alternative hypothesis:
`p >(4)/(1000)=0.004`

And the most reasonable choice for the options given it seems

C. H0: p = 0.004

H1: p > 0.004

Because in the null hypothesis we always need to have an equal sign and the optiosns A, B and D are not satisfying this condition