Please enable JavaScript.
Coggle requires JavaScript to display documents.
Chapter 7: The Distribution of Sample Means - Coggle Diagram
Chapter 7: The Distribution of Sample Means
What if you were asked to estimate a population based on a sample? Ex. Take 5 colored balls out of 500 or take 20 balls? 20 balls is more likely to be a more accurate representation of the population.
The law of large numbers. As the sample size increases, the difference between the sample mean and population mean decreases.
Sampling error. The difference or discrepancy between a sample statistic and its population parameter.
Samples are different. If you take two samples from the same population, they are not likely to be the same. How can you tell which sample gives the best estimate of the total population?
Distribution of sample means. The collection of sample means of all possible random samples of size n that exists within a population.
If a population has 100 samples and the sample size is 1, the probability of selecting any sample is 1/100.
Sampling distribution. Distribution of statistics of collecting all possible samples of specific size from a population.
What are characteristics of sample means?
2) The pile of sample means tends to form a normal distribution.
3) The larger the sample size (n), the closer the sample means will be to the population means
1) Should pile up around the population means.
Central limit theorem. For any population of mean ยต and standard deviation ๐, the distribution of sample means of sample size n will have a mean of ยต and a standard deviation of ๐/โn and will approach a normal distribution as n approaches infinity.
By the time a sample size approaches 30, then a distribution of sample means is almost perfectly normal
A distribution of sample means is also assumed to be normal if the population has a normal distribution
Expected value of M. The mean of the distribution of sample means is expected to be the mean of the population.
The standard error of M, ๐m, the standard deviation of the distribution of sample means.
Provides a measure of how much difference exists between one sample mean and another.
Measures how much an individual sample represents the entire population.
Standard error formula is ๐/โn
Whenever you have a question about the probability of a sample mean, you must use the distribution of sample means
Z-score for sample means. Can use a z-score to describe the exact location of a sample mean within a distribution of sample means.
Important. When computing the Z-score for a sample mean, you must use the standard error of M, ๐m.