By Stokes' theorem, the line integral of over
is given by the surface integral of the curl of
over
, where
is the region of intersection of the plane
and the cylinder
with
having positive/upward orientation.
Parameterize by
with and
.
Take the normal vector to to be
The curl of is
Then the line integral is equivalent to
Answer:
A. We need to conduct a hypothesis in order to test the claim that the true proportion of inaccurate orders p is 0.1.
B. Null hypothesis:
Alternative hypothesis:
C.
D.
E. Fail to the reject the null hypothesis
F. So the p value obtained was a very high value and using the significance level given we have
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the true proportion of inaccurate orders is not significantly different from 0.1.
Step-by-step explanation:
Data given and notation
n=362 represent the random sample taken
X=33 represent the number of orders not accurate
estimated proportion of orders not accurate
is the value that we want to test
represent the significance level
Confidence=95% or 0.95
z would represent the statistic (variable of interest)
represent the p value (variable of interest)
A: Write the claim as a mathematical statement involving the population proportion p
We need to conduct a hypothesis in order to test the claim that the true proportion of inaccurate orders p is 0.1.
B: State the null (H0) and alternative (H1) hypotheses
Null hypothesis:
Alternative hypothesis:
When we conduct a proportion test we need to use the z statistic, and the is given by:
(1)
The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value
.
C: Find the test statistic
Since we have all the info required we can replace in formula (1) like this:
D: Find the critical value(s)
Since is a bilateral test we have two critical values. We need to look on the normal standard distribution a quantile that accumulates 0.025 of the area on each tail. And for this case we have:
P value
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level provided . The next step would be calculate the p value for this test.
Since is a bilateral test the p value would be:
E: Would you Reject or Fail to Reject the null (H0) hypothesis.
Fail to the reject the null hypothesis
F: Write the conclusion of the test.
So the p value obtained was a very high value and using the significance level given we have
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the true proportion of inaccurate orders is not significantly different from 0.1.