Problema Solution
Statistics & Probability:
A researcher conducted a study of the access speed of 45 hard drives and concluded that his maximum error of estimate was 28. If he were to conduct a second study to reduce the maximum error of estimate to 7, about how many hard drives should he include in his new sample?
Select one:
a. 720
b. 45
c. 90
d. 180
Please can anyone show me the working for this question. The answer in my book is a.720. However, I really do not know how to get to that answer. Thanks.
Answer provided by our tutors
The error of estimate is calcaulated as the square root of the sum of the differences from the mean divided by the number of samples:
E = SQRT(SUM(xi-Xest)/n)
where 'xi represents one measurement and Xest is the estimated value
For the study already completed we know that n=45 and E=28 so we can solve for the SUM() portion as follows:
28 = SQRT(SUM()/45)
784 = SUM()/45
SUM() = 45 * 784 = 35280
Now, assuming that the data remains, on average, scattered around the estimated value in the same manner, the magnitude of SUM() will no change and we can calculuate a new 'n' for the desired value of E:
7 = SQRT(35280/n)
49 = 35280/n
n = 35280/49 = 720