The following table shows the total points scored in the 10 national football league games played during week 1 of the 2016 session

Question

23 25 33 51 62
24 31 58 47 49
Based on the above data
A calculate population mean?
B calculate sampling error using the first three games in the first raw as a sample?
C calculate the sampling error using all five games in the first row as a sample ?
D how does increasing the sample size affect the sampling error?

Answer 1

A) The population mean is calculated by adding up all the scores and dividing by the total number of games:

Population mean = (23 + 25 + 33 + 51 + 62 + 24 + 31 + 58 + 47 + 49) / 10

Population mean = 385 / 10

Population mean = 38.5

Therefore, the population mean is 38.5.

B) To calculate the sampling error using the first three games in the first row as a sample, we need to first calculate the sample mean, which is the average of the three scores:

Sample mean = (23 + 25 + 33) / 3

Sample mean = 81 / 3

Sample mean = 27

Then, we calculate the sampling error using the formula:

Sampling error = Population mean - Sample mean

Sampling error = 38.5 - 27

Sampling error = 11.5

Therefore, the sampling error using the first three games in the first row as a sample is 11.5.

C) To calculate the sampling error using all five games in the first row as a sample, we first need to calculate the sample mean:

Sample mean = (23 + 25 + 33 + 51 + 62) / 5

Sample mean = 194 / 5

Sample mean = 38.8

Then, we calculate the sampling error using the formula:

Sampling error = Population mean - Sample mean

Sampling error = 38.5 - 38.8

Sampling error = -0.3

Therefore, the sampling error using all five games in the first row as a sample is -0.3.

D) Increasing the sample size generally decreases the sampling error, as long as the sample is selected randomly and is representative of the population. This is because as the sample size increases, the sample mean becomes more accurate and better reflects the population mean. However, there is a point of diminishing returns, where increasing the sample size further does not significantly decrease the sampling error.