Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Explore thousands of questions and answers from a knowledgeable community of experts on our user-friendly platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
From the test the parson wants, and the sample data, we build the test hypothesis and find the p-value.
Suppose someone wants to claim that more than 55% of adult Catholics in the United States are in favor of allowing women to become priests.
At the null hypothesis, it is tested that the proportion is of at most 55%, that is:
[tex]H_0: p \leq 0.55[/tex]
At the alternative hypothesis, it is tested that the proportion is of more than 55%, that is:
[tex]H_1: p > 0.55[/tex]
Since we are testing only one proportion, it is a one-sample test. Since we are testing only if the proportion is higher/lower, in this case higher, than a value, it is a one-tailed test.
P-value:
To find the p-value of the test, we first have to find the test statistic.
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the nu
0.55 is tested at the null hypothesis:
This means that [tex]\mu = 0.55, \sigma = \sqrt{0.55*0.45}[/tex]
From the sample:
Survey of 507, 59% answer yes, thus: [tex]n = 507, X = 0.59[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.59 - 0.55}{\frac{\sqrt{0.55*0.45}}{\sqrt{507}}}[/tex]
[tex]z = 1.81[/tex]
P-value from the test statistic:
The p-value of the test is the probability of finding a sample proportion above 1.81, which is 1 subtracted by the p-value of z = 1.81.
Looking at the z-table, z = 1.81 has a p-value of 0.9649.
1 - 0.9649 = 0.0351.
Thus, the p-value of the test is of 0.0351.
For another example of a similar problem, you can check https://brainly.com/question/24166849
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.
