Answer:
And if we find the limits we got:
So then the 95% confidence interval would be (72.0,80.0)
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=49 represent the original sample size
Confidence =95% or 0.95
ME=4 represent the margin of error.
Solution to the problem
The confidence interval for the mean is given by the following formula:
(1)
The margin of error is defined as:
The formula for the confidence interval is equivalent to:
And if we find the limits we got:
So then the 95% confidence interval would be (72.0,80.0)