Assume x=x(t) and y=y(t). find dx/dt if x^2(y-6) = 12y + 3 and dy/dt = 2 when x = 5 and y = 12

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:

At the alternative hypothesis, it is tested that the proportion is of more than 55%, that is:

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:

In which X is the sample mean, is the value tested at the nu

0.55 is tested at the null hypothesis:

This means that

From the sample:

Survey of 507, 59% answer yes, thus:

Value of the test statistic:

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