Author Question: Suppose a park ranger wishes to collect some data from the State Park he works in to asses if the ... (Read 378 times)

anshika · **on:** Jul 24, 2018

Suppose a park ranger wishes to collect some data from the State Park he works in to asses if the proportion of trees in the park that are in need of pruning is significantly higher than 5. He will test the hypotheses H0: p = 0.05 vs. Ha: p > 0.05 . After a week of hard work, randomly selecting and inspecting trees throughout the entire park, the park ranger found that 7 of the trees in the sample were in need of pruning. Think about the park ranger's job when answering the following question. Is the difference between the observed percentage of 7 and the hypothesized value of 5 practically significant?

Question 2

Suppose a park ranger wishes to collect some data from the State Park he works in to asses if the proportion of trees in the park that are in need of pruning is significantly higher than 5. He will test the hypotheses H0: p = 0.05 vs. Ha: p > 0.05 . After a week of hard work, randomly selecting and inspecting trees throughout the entire park, the park ranger found that 7 of the trees in the sample were in need of pruning. Explain in your own words why the results of the test were so different, even though the sample proportion was 7 in both cases.

mistyjohnson · **Reply #1 on:** Jul 24, 2018

Answer to Question 1

Probably not. The park ranger and his crew will have to go out and prune those trees, but the difference between 5 and 7 percent probably does not impact their job. If the percentage were actually, say, 20 percent, they would have to hire more people to accomplish their task.

Answer to Question 2

The p-values for the two tests were very different, therefore resulting in opposite decisions. The sample size plays an important role in hypothesis testing, since it directly affects the standard error. A larger sample size will result in a smaller standard error. With the smaller standard error, the difference between 5 and 7 becomes statistically significant.