Question

A hypnosis program designed to help individuals quit smoking claims a 57% success rate. A consumer watch group suspects that this claim is high and randomly selects 50 individuals who have completed the program in order to conduct a hypothesis test. What are the appropriate null and alternative hypotheses?

a) H0: p = 0.57 vs. Ha: p < 0.57
b) H0: p = 0.57 vs. Ha: p > 0.57
c) H0: p = 0.57 vs. Ha: p ≠ 0.57
d) H0: p < 0.57 vs. Ha: p > 0.57

Answer 1

For this case we are trying to proof if the true proportion of individuals that quit smoking is higher than 0.57 (alternative hypothesis) and the system of hypothesis are:

Null hypothesis:
`p \leq 0.57`

Aternative hypothesis:
`p>0.57`

b) H0: p = 0.57 vs. Ha: p > 0.57

Explanation:

Previous concepts

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".

Solution to the problem

For this case we are trying to proof if the true proportion of individuals that quit smoking is higher than 0.57 (alternative hypothesis) and the system of hypothesis are:

Null hypothesis:
`p \leq 0.57`

Aternative hypothesis:
`p>0.57`

b) H0: p = 0.57 vs. Ha: p > 0.57