For a population with a mean of (mew) = 50 and a standard deviation of 10, how much error, on average, would you expect between the sample mean (M) and the poulation mean for:
a) a sample of n=4 scores
b) a sample of n=16 scores
c) a sample of n=25 scores
Are the sample mean (M) and population means different? How do you find M? I don't understand this question...Please help me!
The inequality for the graph can be expressed as
32 ≤ r ≤ m
where r is the minimum range of the scores in any of the games and m is the maximum range.
What is the value of m?
To calculate the average error between the sample mean (M) and the population mean (μ) for a given sample size (n), you can use the formula for the standard error of the mean (SEM), which is the standard deviation of the sample mean. The formula is given by SEM = σ / √n, where σ represents the population standard deviation and n is the sample size. In this case, the population standard deviation (σ) is given as 10.
Now, let's calculate the average error for each sample size:
a) For a sample of n = 4 scores:
SEM = 10 / √4 = 10 / 2 = 5
b) For a sample of n = 16 scores:
SEM = 10 / √16 = 10 / 4 = 2.5
c) For a sample of n = 25 scores:
SEM = 10 / √25 = 10 / 5 = 2
The average error between the sample mean and the population mean is represented by the standard error of the mean (SEM). This indicates how much the sample mean is likely to deviate from the population mean on average. Smaller SEM values indicate less error and greater precision in estimating the population mean.
Regarding the difference between the sample mean (M) and the population mean (μ), they are two distinct concepts. The population mean (μ) is the average value of a variable in the entire population, while the sample mean (M) is the average value of a variable in a specific sample drawn from the population.
To find the sample mean (M), you simply calculate the average of the individual scores in the sample. Add up all the scores and divide the sum by the number of scores in the sample. It is important to note that the sample mean (M) is an estimate or approximation of the population mean (μ) based on the data collected in the sample. The difference between the two represents the sampling error, which is inherent in estimating population parameters from sample data.