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Answer:
a) The 99% confidence interval would be given by (24.409;24.979)
b) n=464
Step-by-step explanation:
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".
Part a
The confidence interval for the mean is given by the following formula:
(1)
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(0.025,46)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 95% confidence interval would be given by (503.01;546.99)
Part b
The margin of error is given by this formula:
(1)
And on this case we have that ME =7 msec, we are interested in order to find the value of n, if we solve n from equation (1) we got:
(2)
The critical value for 95% of confidence interval is provided, from part a, replacing into formula (2) we got:
So the answer for this case would be n=464 rounded up to the nearest integer