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monkeyrose1999
21.04.2020 •
Mathematics
It is desired to estimate the mean GPA of each undergraduate class at a large university. How large a sample is necessary to estimate the GPA within at the confidence level? The population standard deviation is . If needed, round your final answer up to the next whole number.
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Ответ:
So the answer for this case would be n=154 rounded up to the nearest integer
Step-by-step explanation:
Assuming the following question: It is desired to estimate the mean GPA of each undergraduate class at a large university. How large a sample is necessary to estimate the GPA within 0.25 at the 99% confidence level? The population standard deviation is 1.2. If needed, round your final answer up to the next whole number.
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".
s represent the sample standard deviation
n represent the sample size
Solution to the problem
The margin of error is given by this formula:
And on this case we have that ME =0.25 and we are interested in order to find the value of n, if we solve n from equation (a) we got:
The critical value for 99% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.005;0;1)", and we got
, replacing into formula (b) we got:
So the answer for this case would be n=154 rounded up to the nearest integer
Ответ:
hi there
Step-by-step explanation:
i said hello