5 + (9) (6) - 4 = I want an explanation too not too long.
1 answer:
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Part (a)
The domain is the set of allowed x inputs of a function.
The graph shows that x = 0 is not allowed because of the vertical asymptote located here. It seems like any other x value is fine though.
<h3>Domain: set of all real numbers butTo write this in interval notation, we can say which is the result of poking a hole at 0 on the real number line.
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The range deals with the y values. The graph makes it seem like it stretches on forever in both up and down directions. If this is the case, then the range is the set of all real numbers.
<h3>Range: Set of all real numbers</h3>In interval notation, we would say which is almost identical to the interval notation of the domain, except this time of course we aren't poking at hole at 0.
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Part (b)
<h3>The x intercepts are x = -4 and x = 4</h3>We can compact that to the notation
These are the locations where the blue hyperbolic curve crosses the x axis.
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Part (c)
<h3>Answer: There aren't any horizontal asymptotes in this graph.</h3>Reason: The presence of an oblique asymptote cancels out any potential for a horizontal asymptote.
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Part (d)
The vertical asymptote is located at x = 0, so the equation of the vertical asymptote is naturally x = 0. Every point on the vertical dashed line has an x coordinate of zero. The y coordinate can be anything you want.
<h3>Answer: x = 0 is the vertical asymptote</h3>=======================================================
Part (e)
The oblique or slant asymptote is the diagonal dashed line.
It goes through (0,0) and (2,6)
The equation of the line through those points is y = 3x
If you were to zoom out on the graph (if possible), then you should notice the branches of the hyperbola stretch forever upward but they slowly should approach the "fencing" that is y = 3x. The same goes for the vertical asymptote as well of course.
<h3>Answer: Oblique asymptote is y = 3x</h3>
Answer:
a) The 99% confidence interval is given by (0.198;0.242).
b) Based on the p value obtained and using the significance level assumed we have
so we can conclude that we fail to reject the null hypothesis, and we can said that at 1% of significance the proportion of people who are rated with Excellent/Good economy conditions not differs from 0.24. The interval also confirms the conclusion since 0.24 it's inside of the interval calculated.
c)
Step-by-step explanation:
<em>Data given and notation </em>
n=2362 represent the random sample taken
X represent the people who says that they would watch one of the television shows.
estimated proportion of people rated as Excellent/Good economic conditions.
is the value that we want to test
represent the significance level
z would represent the statistic (variable of interest)
represent the p value (variable of interest) <em>
</em>
<em>Concepts and formulas to use </em>
We need to conduct a hypothesis in order to test the claim that 24% of people are rated with good economic conditions:
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
.
Part a: Test the hypothesis
<em>Check for the assumptions that he sample must satisfy in order to apply the test </em>
a)The random sample needs to be representative: On this case the problem no mention about it but we can assume it.
b) The sample needs to be large enough
np = 2362x0.22=519.64>10 and n(1-p)=2364*(1-0.22)=1843.92>10
Condition satisfied.
<em>Calculate the statistic</em>
Since we have all the info requires we can replace in formula (1) like this:
The confidence interval would be given by:
The critical value using and
would be
. Replacing the values given we have:
So the 99% confidence interval is given by (0.198;0.242).
Part b
<em>Statistical decision </em>
P value method or p value approach . "This method consists on 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 is . The next step would be calculate the p value for this test.
Since is a bilateral test the p value would be:
So based on the p value obtained and using the significance level assumed we have
so we can conclude that we fail to reject the null hypothesis, and we can said that at 1% of significance the proportion of people who are rated with Excellent/Good economy conditions not differs from 0.24. The interval also confirms the conclusion since 0.24 it's inside of the interval calculated.
Part c
The confidence level assumed was 99%, so then the signficance is given by