Question

In a hypothesis test involving the population proportion, which of the following would be an acceptable formulation?

Ho: p=0.25 Ha: vs p not equal0.25

none of these

Ho: p = 0.25 Vs Ha: p< 0.25

Ho: p = 0.25 vs Ha: p>0.25

please what is the answer?

Answer 1

1) Ho: p=0.25 Ha: vs p not equal to 0.25

2) none of these

3) Ho: p = 0.25 Vs Ha: p < 0.25

4) Ho: p = 0.25 vs Ha: p > 0.25

The options coloured in green are acceptable in a hypothesis testing involving the population proportion. Note that, a null hypothesis is one which we try to disprove while the alternative hypothesis consists of the opposite. We assume that under the null hypothesis, there should be no change in the outcome and whatever happens is random, owing to chance causes while in the alternative hypothesis, we hypothesize that there is indeed some change owing to some factors. Hence, we can have all three hypothesis.

Options 1,3, 4 correspond to both tailed test, left tailed test and right tailed test. In a both tailed test, a change in either direction is hypothesised.

In a left tailed test, a decrease is hypothesized.

In a right tailed test, an increase is hypothesized.

And all three hypotheses are plausible and acceptable.