| Group | n | Mean | SD |
|---|---|---|---|
| A | 18 | 3.39 | 0.47 |
| B | 14 | 3.86 | 0.51 |
Sample Exam 2
Part A: Conceptual (Multiple Choice)
What does a small p-value indicate?
The null hypothesis is true
Strong evidence against the null hypothesis
The sample size is small
The model has no error
What does R² measure?
The slope of the regression line
The variability in the predictor
The proportion of variability explained by the model
The p-value of the test
A Type I error occurs when:
You fail to reject a false null hypothesis
You reject a true null hypothesis
You accept a false alternative hypothesis
The sample size is too large
Which test is used to compare more than two group means?
t-test
ANOVA
Chi-square
Regression
In regression, what does b₁ represent?
The average of Y
The predicted value when X = 0
The average change in Y for a one-unit increase in X
The variance of Y
Part B: Short Answer
Explain the difference between a simple and a complex model.
What is a null distribution and why is it important?
What does it mean if a result is statistically significant at α = 0.05?
Part C: Interpretation
A regression analysis gives:
| Terms | Estimate | Std Error | t value | Pr(>|t|) |
|---|---|---|---|---|
| (Intercept) | 3.59656 | 0.08410 | 42.765 | < 2e-16 |
| x | -0.20124 | 0.06651 | [t] | 0.00505 |
Answer:
Interpret the slope
Find the missing [t]
State whether the result is significant
Write the equation for the regression (use \(y\) as the outcome variable):
Find and interpret the value of \(y\) when \(x\) is 0.75.
An ANOVA test gives:
| SS | df | MS | F | PRE | p | |
|---|---|---|---|---|---|---|
| Model (error reduced) | 5.10 | 4.00 | [a] | [F] | [R2] | 0.0004 |
| Error (from model) | 3.70 | 23.00 | [b] |
Answer:
Find the missing [F] value.
How many groups are being abalyzed?
What are the hypotheses this table is testing?
What is the conclusion of the test?
Find the missing [R2] and interpret it.
Part D: Applied Thinking
A researcher runs 10 different tests at α = 0.05.
What problem might occur?
How could it be addressed?
You observe a strong relationship in a sample, but the p-value is large. Why might this happen?
Part E: Data Reasoning
Given a contingency table (Gender × Job):
What test should be used?
What would the null hypothesis be?
The following summary of \(y\) is given:
What is the differnce of the sample means?
What is the standard error of the differnce of the sample means?
Compute \(t=\frac{\bar x_B-\bar x_A}{SE}\).
what is the distribution of \(t\), if we assume the group variances are equal?
Write a conclusion if the \(p\text{-value}=0.012\) and \(H_a: \mu_A\ne\mu_B\).
What is the Cohen’s \(d\) and what does it mean?
Write the lm equation for Y~X and the estimate values for \(\beta_0\) and \(\beta_1\)?
Challenge Questions
Explain how the t-distribution differs from the normal distribution.
Why do we use an F-test instead of multiple t-tests in ANOVA?