2.8.1
By definition of the derivative,
We have
and
Combine these fractions into one with a common denominator:
Rationalize the numerator by multiplying uniformly by the conjugate of the numerator, and simplify the result:
Now divide this by <em>h</em> and take the limit as <em>h</em> approaches 0 :
3.1.1.
Differentiate one term at a time:
• power rule
The last two terms are constant, so their derivatives are both zero.
So you end up with
Answer:
We need to conduct a hypothesis in order to test the claim that the true proportion is 0.36 so then we need to conduct a two tailed test, the system of hypothesis are.:
Null hypothesis:
Alternative hypothesis:
Since is a bilateral test the p value would be:
Step-by-step explanation:
Data given and notation n
n represent the random sample taken
estimated proportion of interest
is the value that we want to test
z would represent the statistic (variable of interest)
represent the p value (variable of interest)
Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the true proportion is 0.36 so then we need to conduct a two tailed test, the system of hypothesis are.:
Null hypothesis:
Alternative hypothesis:
When we conduct a proportion test we need to use the z statisitc, 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 .
Calculate the statistic
For this case the statistic is given:
Statistical decision
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 next step would be calculate the p value for this test.
Since is a bilateral test the p value would be: