Answer:
So then the confidence interval for the difference of means is 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 mean for the age of grandmother
represent the mean for the age of grandfather
represent the sample deviation for the age of grandmother
represent the sample deviation for the age of grandfather
Solution to the problem
For this case the confidence interval is given by:
In order to calculate the critical value we need to find first the degrees of freedom, given by:
Since the Confidence is 0.95 or 95%, the value of and
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,18)".And we see that
And replacing we got:
So then the confidence interval for the difference of means is given by: