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Population A and Population B both have a mean height of 70.0 inches with an SD of 6.0. A random sample of 50 people is picked from population A, and random sample of 20 people is selected from Population B. Which sample mean will probably yield a more accurate estimate of its population mean? Why?

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Answer:

Sample mean from population A has probably more accurate estimate of its population mean than the sample mean from population B.

Step-by-step explanation:

To yield a more accurate estimate of the population mean, margin of error should be minimized.

margin of error (ME) of the mean can be calculated using the formula

ME=[tex]\frac{z*s}{\sqrt{N} }[/tex] where

  • z is the corresponding statistic in the given confidence level(z-score or t-score)
  • s is the standard deviation of the sample (or of the population if it is known)
  • N is the sample size

for a given confidence level, and the same standard deviation, as the sample size increases, margin of error decreases.

Thus, random sample of 50 people from population A, has smaller margin of error than the sample of 20 people from population B.

Therefore, sample mean from population A has probably more accurate estimate of its population mean than the sample mean from population B.

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