Respuesta :
Using the z-distribution, as we are working with a proportion, it is found that since the test statistic is greater than the critical value for the right-tailed test, the sample provides convincing evidence that a majority of local residents oppose hunting on Morro Bay.
What are the hypothesis tested?
At the null hypothesis, we test if no more than a majority of local residents oppose hunting on Morro Bay, that is:
[tex]H_0: p \leq 0.5[/tex]
At the alternative hypothesis, we test if more than a majority of local residents oppose hunting on Morro Bay, that is:
[tex]H_1: p > 0.5[/tex]
What is the test statistic?
The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
- [tex]\overline{p}[/tex] is the sample proportion.
- p is the proportion tested at the null hypothesis.
- n is the sample size.
In this problem, the parameters are:
[tex]p = 0.5, n = 750, \overline{p} = \frac{560}{750} = 0.7467[/tex]
Hence, the value of the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.7467 - 0.5}{\sqrt{\frac{0.5(0.5)}{750}}}[/tex]
[tex]z = 13.5[/tex]
What is the decision?
The critical value for a right-tailed test, as we are testing if the proportion is greater than a value, with a significance level of 0.01, is of [tex]z^{\ast} = 2.327[/tex].
Since the test statistic is greater than the critical value for the right-tailed test, the sample provides convincing evidence that a majority of local residents oppose hunting on Morro Bay.
More can be learned about the z-distribution at https://brainly.com/question/16313918
