The Distribution of Sample Means

These flashcards cover key concepts related to the distribution of sample means, sampling error, standard error, and the implications of sample size in statistical research.

What is the main purpose of using the sample mean in research studies instead of a single score?

The sample mean is used to answer questions about the population based on larger samples.

What is a key challenge encountered when working with samples?

A sample provides an incomplete picture of the population.

What is the sampling distribution?

The distribution of a statistic across an infinite number of samples.

What shapes the distribution of sample means?

Sample means pile up around the population mean.

What is the expected value of M?

It is the mean of the distribution of sample means, which is identical to the population mean.

What is sampling error?

The difference between sample statistics and the corresponding population parameters.

What does the Standard Error (SE) measure?

It measures how well a sample mean represents the overall population mean.

How does sample size affect sampling error?

Generally, as the sample size increases, the sampling error decreases.

What happens to the shape of the distribution of sample means as the sample size increases?

The distribution approaches a normal distribution.

What two conditions can make the distribution of sample means almost perfectly normal?

1. The population from which samples are selected is a normal distribution. 2. The sample size is 30 or more.

What factors determine the magnitude of the standard error?

The size of the sample and the standard deviation of the population.

If a sample mean is expected to be close to the population mean, which symbol is used to represent this mean of the distribution of sample means?

μM, although it equals μ.

Why is the standard error considered a valuable measure in research?

It specifies how much error to expect between the sample mean and the population mean.

How can researchers reduce sampling error effectively?

By increasing the sample size up to around n = 30.

What role do z-scores play in working with sample means?

They help calculate probabilities and standard deviations for the sample means.

What is the probability of obtaining a random sample with a mean greater than a certain value based on the sample mean and standard error?

It is calculated using the z-score and the z-table.

What is the relationship between sample size and the accuracy of sample means in representing the population mean?

Larger sample sizes produce means that cluster closer to the population mean.