Problem

Using the information above, choose the correct conclusion for this hypothesis test.
- $H_{0}: p=0.15 ; H_{a}: p> 0.15$
- The $p$-value for this hypothesis test is 0.002 .
- The level of significance is $\alpha=0.025$

Answer

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Answer

Final Answer: \(\boxed{\text{Reject the null hypothesis in favor of the alternative hypothesis}}\)

Steps

Step 1 :The null hypothesis $H_{0}$ states that the population proportion $p$ is equal to 0.15.

Step 2 :The alternative hypothesis $H_{a}$ states that the population proportion $p$ is greater than 0.15.

Step 3 :The $p$-value is the probability of obtaining a result as extreme as, or more extreme than, the observed data, assuming that the null hypothesis is true.

Step 4 :If the $p$-value is less than the level of significance $\alpha$, we reject the null hypothesis in favor of the alternative hypothesis.

Step 5 :In this case, the $p$-value is 0.002, which is less than the level of significance $\alpha=0.025$.

Step 6 :Therefore, we reject the null hypothesis in favor of the alternative hypothesis.

Step 7 :Final Answer: \(\boxed{\text{Reject the null hypothesis in favor of the alternative hypothesis}}\)

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