PSY 230: Finals Study Guide

How does confidence level affect the width of a confidence interval?

→ As confidence level increases, the confidence interval becomes wider because the critical Z value increases.

Which factors affect the margin of error of a confidence interval about the mean?

→ Sample size
→ Confidence level
→ Standard deviation

→ Sample mean, median, and mode do not affect margin of error.

What does a confidence interval tell us?

→ A plausible range of values for the true population parameter.

What does a confidence interval NOT tell us?

→ It does not mean there is a probability (e.g., 95%) that the true parameter lies in the interval.

What are the appropriate conclusions from a hypothesis test

• Reject the null hypothesis

• Fail to reject the null hypothesis

• We never accept the null hypothesis

Hypotheses for a left-tailed test for the mean

• H₀: μ = μ₀

• Hₐ: μ < μ₀

Hypotheses for a right-tailed test for the mean

• H₀: μ = μ₀

• Hₐ: μ > μ₀

Hypotheses for a two-tailed test for the mean

• H₀: μ = μ₀

• Hₐ: μ ≠ μ₀

Hypotheses for a left-tailed test for the proportion

• H₀: p = p₀

• Hₐ: p < p₀

Hypotheses for a right-tailed test for the proportion

• H₀: p = p₀

• Hₐ: p > p₀

Hypotheses for a two-tailed test for the proportion

• H₀: p = p₀

• Hₐ: p ≠ p₀

What is one constant with the null hypothesis?

It always contains an equals sign (=)

If we want to prove a hypothesis, which hypothesis must it be?

• The alternative hypothesis

What does a p-value represent? How is it used?

• The probability of observing results as extreme as the sample assuming the null hypothesis is true

• If p ≤ α → Reject H₀

• If p > α → Fail to reject H₀

How do you compute the p-value for a Z-test?

• Left-tailed: Area to the left of Z

• Right-tailed: Area to the right of Z

• Two-tailed: Double the tail area beyond |Z|

If we are running a hypothesis test for the population proportion, what assumptions do we need to validate prior to running a Z test?

np ≥ 5 and nq ≥ 5

As the degrees of freedom increases, what happens to the Student’s T-Distribution?

It approaches the standard normal (Z) distribution.

As the degrees of freedom increases, what happens to my critical T-values?

They get smaller and approach critical Z values.

What are the assumptions required to use the Student’s T-distribution when performing a hypothesis test or confidence interval about the mean?

→ σ is unknown, population is normal, no outliers, and using it for applicable inference (mean CI/tests, correlation)

What is the main indicator whether we should use the Z or T distribution when we are running a hypothesis test for the mean?

→ Whether the population standard deviation (σ) is known (Z) or unknown (T).

Describe the following correlations:

a. r = 0.95
→ Strong, positive

PSY 230 Final Exam Study Guide

b. r = 0.14
→ Weak, positive

PSY 230 Final Exam Study Guide

c. r = -0.25
→ Weak, negative

PSY 230 Final Exam Study Guide

d. r = -0.91
→ Strong, negative

If a correlation between two variables is positive, what relationship do the variables have as they change?

→ As one increases, the other also increases

If a correlation between two variables is negative, what relationship do the variables have as they change?

→ As one increases, the other decreases.

Interpolation

x values within the data range used to build the model.

Extrapolation

x values outside the data range used to build the model.

Regression model predicting height of elementary school kids by age. Appropriate use?

a. Predicting the height of a 2nd grader
→ Appropriate

PSY 230 Final Exam Study Guide

b. Predicting the height of a 9th grader
→ Not appropriate

PSY 230 Final Exam Study Guide

c. Predicting the height of a 5th grader
→ Appropriate

PSY 230 Final Exam Study Guide

d. Predicting the height of an adult
→ Not appropriate

What are the null and alternative hypotheses used when running a One-Way ANOVA Test?

→ H₀: all group means are equal
→ Hₐ: at least one mean is different

What are the assumptions required to run a One-Way ANOVA Test?

→ At least 3 samples, independence, normality, equal variances

Type I Error (False Positive)

Definition:
→ Rejecting a true null hypothesis
→ Probability = α

Example (Medical Test)

• H₀: The patient does not have a disease

• Decision: Test says the patient does have the disease

• Reality: Patient is actually healthy

Type II Error (False Negative)

Definition:
→ Failing to reject a false null hypothesis
→ Probability = β

Example (Medical Test)

• H₀: The patient does not have a disease

• Decision: Test says the patient does not have the disease

• Reality: Patient actually has the disease

Statistical significance

→ p-value ≤ α
→ Result unlikely due to chance

Practical significance

• → Is the result meaningful in the real world?

🚨 A result can be statistically significant but not practically important.

If a null value is inside a confidence interval

Fail to reject H₀

If a null value is outside a confidence interval

Reject H₀