Module 5: Probability, z-Scores, and Sample Distributions

According to the central limit theorem, if the population of scores is normally distributed, the sampling distribution of means will be normally distributed ____________.

with any sample size

A professor is interested in the amount of time students take to complete a homework assignment. She takes a sample of students (n = 10) and finds that the mean is 120 minutes, with a variance of 42.25. What is the estimate of the mean of the sampling distribution of means?

120

A sample consists of the following scores measuring anxiety: 3, 5, 3.25, 4.3, 7. What is the estimate of the mean of the sampling distribution of the mean?

4.51

What values can z-scores theoretically take on?

a z-score between −0.5 and 1

Probability distributions ____________.

allow for a way to estimate the probability of a value

What happens when you are studying a single effect but you gather multiple samples?

each sample will have a different mean.

How might replicating a study be related to the central limit theorem?

having multiple samples (of the same n) can give you a better idea of the shape of the sampling distribution of the mean, rather than only assuming.

Most often, the sampling distribution is ____________.

hypothetical and not actually known

There are differences in the sampling distribution each time a sample is drawn due to ____________.

sampling error

What benefit might a data set with 25 observations have over a data set with 5 observations?

the data set with 25 observations has more of a chance to be representative of the population.

How are z-scores and percentile related to one another?

the percentile is the area under the curve to the left of the z-score

Why do we use the standard normal distribution in statistics?

to put different values on the same, standardized scale for comparison