Graph the function below: y = 32 +1
1 answer:
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Answer:
1/2, 3
Step-by-step explanation:
This is a pretty involved problem, so I'm going to start by laying out two facts that our going to help us get there.
- The Fundamental Theorem of Algebra tells us that any polynomial has <em>as many zeroes as its degree</em>. Our function f(x) has a degree of 4, so we'll have 4 zeroes. Also,
- Complex zeroes come in pairs. Specifically, they come in <em>conjugate pairs</em>. If -2i is a zero, 2i must be a zero, too. The "why" is beyond the scope of this response, but this result is called the "complex conjugate root theorem".
In 2., I mentioned that both -2i and 2i must be zeroes of f(x). This means that both and
are factors of f(x), and furthermore, their product,
, is <em>also</em> a factor. To see what's left after we factor out that product, we can use polynomial long division to find that
I'll go through to steps to factor that second expression below:
Solving both of the expressions when f(x) = 0 gets us our final two zeroes:
So, the remaining zeroes are 1/2 and 3.
Answer:
a)
If we compare the p value obtained 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 proportion of rejected items is less than 0.03.
b) We can use a 95 percent upper confidence interval.
On this case we want a interval on this form :
So the critical value would be on this case and we can use the following excel code to find it: "=NORM.INV(1-0.05,0,1)"
We found the upper limit like this:
And the interval would be:
And since our value (0.02) is contained in the interval We fail to reject the hypothesis that p=0.03
Step-by-step explanation:
Part a
Data given and notation
n=500 represent the random sample taken
X=10 represent the number of objects rejected
estimated proportion of objects rejected
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)
Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that 70% of adults say that it is morally wrong to not report all income on tax returns.:
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
.
Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
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 significance level provided . The next step would be calculate the p value for this test.
Since is a one tailed left test the p value would be:
If we compare the p value obtained 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 proportion of rejected items is less than 0.03.
Part b
We can use a 95 percent upper confidence interval.
On this case we want a interval on this form :
So the critical value would be on this case and we can use the following excel code to find it: "=NORM.INV(1-0.05,0,1)"
We found the upper limit like this:
And the interval would be:
And since our value (0.02) is contained in the interval We fail to reject the hypothesis that p=0.03