I don't get this question #3
1 answer:
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Answer:
And rounded up we have that n=2663
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The population proportion have the following distribution
Solution to the problem
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by and
. And the critical value would be given by:
The margin of error for the proportion interval is given by this formula:
(a)
And on this case we have that and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
We can assume an estimated proportion of since we don't have prior info provided. And replacing into equation (b) the values from part a we got:
And rounded up we have that n=2663
You can go through the effort of determining the zero of the function analytically and evaluating an analytic expression for the derivative at that point, or you can let a graphing calculator do that heavy lifting. Since the numbers have to be "nice" for your equation to have the desired form, it is easy to know what to round to in the event that is necessary (it isn't).
We find the positive zero-crossing at x=2, and the slope of the curve at that point to be 8. Thus the line will have slope -1/8 and can be written as
.. x +8y -2 = 0
We find the positive zero-crossing at x=2, and the slope of the curve at that point to be 8. Thus the line will have slope -1/8 and can be written as
.. x +8y -2 = 0