Answer:
We can estimate the margin of error with this formula:
And the margin of error is given by:
And we can rewrite the margin of error like this:
Where
For 95% of confidence the critical value is
The Standard error would be:
For 99% of confidence the critical value is
And the new margin of error would be:
And then the interval would be given by:
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 (variable of interest)
s represent the sample standard deviation
n represent the sample size
Solution to the problem
The confidence interval for the mean is given by the following formula:
(1)
The 95% confidence interval is given by (66000 , 70000)
We can estimate the mean with this formula:
We can estimate the margin of error with this formula:
And the margin of error is given by:
And we can rewrite the margin of error like this:
Where
For 95% of confidence the critical value is
The Standard error would be:
For 99% of confidence the critical value is
And the new margin of error would be:
And then the interval would be given by: