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07.03.2020 •
Mathematics
How many observations should a time study analyst plan for in an operation that has a standard deviation of .9 minutes per piece if the goal is to estimate the mean time per piece to within .1 minute with a confidence of 95.5 percent
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Ответ:
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".
s represent the sample standard deviation
n represent the sample size
Solution to the problem
The margin of error is given by this formula:
And on this case we have that ME =0.1 and we are interested in order to find the value of n, if we solve n from equation (a) we got:
The critical value for 95.5% of confidence interval now can be founded using the normal distribution. And in excel we can use this formula to find it:"=-NORM.INV(0.023;0;1)", and we got
, replacing into formula (b) we got:
So the answer for this case would be n=4 rounded up to the nearest integer
Ответ: