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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".
Solution to the problem
The confidence interval for the mean is given by the following formula:
(1)
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: "=-NORM.INV(0.025,0,1)".And we see that
Now we have everything in order to replace into formula (1):
Answer:
a) 25
b) 67
c) 97
Step-by-step explanation:
We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
Now, we have to find z in the Ztable as such z has a pvalue of .
So it is z with a pvalue of , so
Now, find the margin of error M as such
In which is the standard deviation of the population and n is the size of the sample. In this problem,
(a) The desired margin of error is $0.10.
This is n when M = 0.1. So
Rounding up to the nearest whole number, 25.
(b) The desired margin of error is $0.06.
This is n when M = 0.06. So
Rounding up, 67
(c) The desired margin of error is $0.05.
This is n when M = 0.05. So
Rounding up, 97