probability

Which statement best describes probability in statistical research?

A numerical measure indicating how likely an event is to occur under given conditions

What is the probability of an event that is certain to occur?

A probability of one showing absolute certainty

If two events cannot occur at the same time, they are considered:

Events that are mutually exclusive and cannot overlap

If P(A) = 0.4 and P(B) = 0.3 for independent events, what is P(A and B)?

(0.12)

Which description best defines a random sample?

A sample chosen so every member of the population has an equal chance of selection

A sampling distribution refers to

The distribution of a statistic formed by repeated samples of the same size

Which of the following is a parameter, not a statistic?

A population mean

Why do sampling distributions differ from one sample to another?

Because each sample may contain different individuals selected from the population

If sample size increases, sampling variability generally:

Decreases because larger samples provide more stable estimates

A sampling distribution of the sample mean represents

All possible sample means computed from samples of the same size

Explain the difference between a mutually exclusive event and an independent event.

Mutually exclusive events cannot occur at the same time—for example, getting heads and tails on one coin toss. Independent events do not influence each other; the outcome of one does not affect the probability of the other.

Why is sampling variability expected when drawing repeated samples from the same population?

Sampling variability occurs because each sample contains different individuals chosen randomly from the population. As a result, sample statistics like the mean naturally fluctuate from sample to sample.

What is the purpose of using probability rules when analyzing events?

Probability rules help researchers calculate likelihoods accurately and combine events logically. They provide a structured way to understand and predict uncertain outcomes.

How does using a random sampling method improve the quality of research results?

Random sampling reduces selection bias because every member of the population has an equal chance of being chosen. This increases the representativeness and generalizability of the findings.

What does a sampling distribution allow researchers to understand about sample statistics?

A sampling distribution shows how a statistic (such as the sample mean) varies across repeated samples. It helps researchers understand expected values, variability, and how reliable a statistic is.