Question

What is the range of sample sizes the research could take from this population without violating conditions required for the application of the formula and the central limit theorem?

Select one:

a. n < 75

b. n > 30

c. 30 < n < 75

d. 30 < N &lt; 50

Answer 1

The Central Limit Theorem says we can use the normal distribution to describe the behavior of a sample mean even if the individual values that make up the sample mean are not normal themselves. But this is only possible if the sample size is “large enough.”, ie. n would have to be at least 30.

Now, n=30 is the benchmark, because once we hit 30 degrees of freedom, the t-values start getting closer and closer to the z-values of the normal distribution.

So, the range of sample sizes, the research could take from this population without violating the conditions, required for implementation of central limit theorem, is option (b) n>30.