Question

If your null and alternative hypothesis are:

H_0 : p = 0
H_A : p > 0

Then the test is: left-tailed or right-tailed?

If we reject the null hypothesis, that would suggest the data has a significant: increasing trend or decreasing trend?

Answer 1

In your hypotheses:

- \( H_0: p = 0 \) (the null hypothesis)
- \( H_A: p > 0 \) (the alternative hypothesis)

This setup indicates that you are testing if the proportion \( p \) is greater than 0. Since the alternative hypothesis specifies that \( p \) is greater than the null hypothesis value, this is a **right-tailed test**.

If you reject the null hypothesis, it suggests that the data has a significant **increasing trend**. This is because rejecting \( H_0 \) implies that you have found sufficient evidence to support that \( p \) is greater than 0, indicating a positive association or increase.