Question

Peter wants to test an assumption on the number of trees that tested positive for a particular infestation. He decides to focus his efforts on examining if more than 12% of trees have been infested. What should Peter state for the null hypothesis and alternative hypothesis

Answer 1

Null hypothesis: p equals 0.12

Alternative hypothesis: p greater than 0.12

Explanation:

Since we are focusing on testing if the proportion of is greater than 12%, we can only reject the null hypothesis if the value is larger. This would be a one-tailed right test. So the null hypothesis and alternative hypothesis would be:

Null hypothesis: p = 0.12

Alternative hypothesis: p > 0.12.

Answer 2

H0 : P ≤ 0.12

H1 : P > 0.12

Explanation:

12% = 12/ 100 = 0.12

Given the population proportion, P = 0.12

The claim is the alternative hypothesis, H1 ; which is to test if more than 12% of trees have been infested.

Hence, the alternative hypothesis will be ;

H1 : P > 0.12

The null hypothesis which is the initial truth is always the opposite of the alternative hypothesis, Therefore, we write our null as ;

The null hypothesis ; H0 : P ≤ 0.12

Therefore, we have :

H0 : P ≤ 0.12

H1 : P > 0.12