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Answer:
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".
represent the sample mean for the sample
population mean
s=4.0 represent the sample standard deviation
n=64 represent the sample size
Assuming the X follows a normal distribution
The sample mean have the following distribution:
The margin of error for the sample mean is given by this formula:
Since we have the sample standard deviation we can estimate the margin of error like this:
The next step would be find the value of ,
and
We can find the degrees of freedom like this:
And we can find the critical value with the following code in excel for example: "=T.INV(0.025,63)" and we got:
And the margin of error would be :