A sample is selected from a population with a mean of µ = 40. If the sample mean is M = 45, which of the following combinations would make the sample mean a good, representative value for the population?​ Question options: a. ​A small sample and a large population standard deviation b. ​A large sample and a large population standard deviation c. ​A small sample and a small population standard deviation d. ​A large sample and a small population standard deviation

Mariyah Bell

Mariyah Bell

Answered question

2022-10-18

A sample is selected from a population with a mean of μ = 40. If the sample mean is M = 45, which of the following combinations would make the sample mean a good, representative value for the population?​
Question options:
a. ​A small sample and a large population standard deviation
b. ​A large sample and a large population standard deviation
c. ​A small sample and a small population standard deviation
d. ​A large sample and a small population standard deviation

Answer & Explanation

jbaekk7q

jbaekk7q

Beginner2022-10-19Added 18 answers

From the central limit theorem, the expected value of sample mean is equal to population mean and the standard deviation of sample mean is population standard deviation by square root of sample size as the large sample size. That is, the standard deviation of sample mean is smaller for the small value of population standard deviation. Hence, the sample mean is a good representative value for the population if large sample size and small population standard deviation.
Thus, the correct option is “d. A large sample and a small population standard deviation”.

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