Question

Imagine that you randomly select a sample of 30 newborn infants and find that their mean weight is 8.1 pounds. The population mean of newborn infants is known to be 7.4 pounds with a standard deviation of 1.1 pounds. Would a sample mean as large as 8.1 be more or less likely if N = 10? Why?

Answer 1

Answer: more likely

Explanation:

Given that :

Population Mean = 7.4

Population standard deviation = 1.1

Sample mean with a sample size of 30 = 8.1

A sample mean of 8.1 will be more likely with a sample size (N) of 10 because, the sampling distribution gets wider with decreasing sample size and narrower with larger sample sizes, hence, sample mean seems to conform with the population mean when the sample size are very large according to the central limit theorem. Hence, since a sample size of 30 results in a sample mean of 8.1, reducing the sample size will either give a similar sample mean or a sample mean further away from the population mean.