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rociomartinez9
28.12.2019 •
Mathematics
One person wants to get a 95% z-confidence interval with a margin of error of at most 15 based on a population standard deviation of 60. what is the minimum sample size needed?
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Ответ:
So the answer for this case would be n=62 rounded up to the nearest integer
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".
n represent the sample size (variable of interest)
Confidence =95% or 0.95
The margin of error is given by this formula:
And on this case we have that ME =15, and we are interested in order to find the value of n, if we solve n from equation (1) we got:
The critical value for 95% of confidence interval is provided,
, replacing into formula (2) we got:
So the answer for this case would be n=62 rounded up to the nearest integer
Ответ:
answer:
fgstep-by-step explanation: