Question

Suppose a population has a mean happiness score of 75 and a standard deviation of 15. Researcher A takes a random sample of 100 participants. Researcher B takes a random sample of 25 participants. Which researcher is more likely to get a sample mean of 80 or higher

Answer 1

Researcher A is more likely to get a sample mean of 80 or higher

Explanation:

The central limit theorem states that if the sample size increases the sampling distribution of the mean approaches normal distribution.The z score would be given by

z= x`- ux/ (σx/√n)

The sample standard deviation is given by 15 / √25 = 3 and 15 / √100 = 1.5

z=75-ux/3/5

Suppose z= 1.96

1.96 = 75 - ux /0.6

1.176- 75= -ux

ux = 73.824

Now Putting values for the second sample

z=75-ux/1.5/10

Suppose z= 1.96

1.96 = 75 - ux /0.15

0.2904- 75= -ux

ux = 74.706

From the above we see that the larger sample size would give a sample mean equal to the population mean .