The following table shows the total points scored in the 10 national football league games played during week 1 of the 2016 session
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?
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.
A. To calculate the population mean, you need to sum up all the values in the table and divide it by the total number of games (which is 10).
Total points scored = 23 + 25 + 33 + 51 + 62 + 24 + 31 + 58 + 47 + 49 = 403
Population mean = Total points scored / Number of games = 403 / 10 = 40.3
Therefore, the population mean is 40.3.
B. To calculate the sampling error using the first three games in the first row as a sample, you need to find the sample mean first. The sampling error is then the difference between the sample mean and the population mean.
Sample mean = (23 + 25 + 33) / 3 = 81 / 3 = 27
Sampling error = Sample mean - Population mean = 27 - 40.3 = -13.3
Therefore, the sampling error using the first three games in the first row as a sample is -13.3.
C. To calculate the sampling error using all five games in the first row as a sample, you need to find the sample mean first. The sampling error is then the difference between the sample mean and the population mean.
Sample mean = (23 + 25 + 33 + 51 + 62) / 5 = 194 / 5 = 38.8
Sampling error = Sample mean - Population mean = 38.8 - 40.3 = -1.5
Therefore, the sampling error using all five games in the first row as a sample is -1.5.
D. Increasing the sample size typically reduces sampling error. As the sample size increases, it becomes more representative of the population, resulting in a smaller difference between the sample mean and the population mean (i.e., reduced sampling error). So, increasing the sample size tends to decrease the sampling error.