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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
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