Question 1

Which of the following best describes a weak positive linear association between two variables?

Accepted Answer

As one variable increases, the other variable tends to increase, but the points are widely scattered around a straight line.

Question 2

In a study examining the relationship between hours studied and exam scores, which variable is the explanatory variable?

Accepted Answer

Hours studied

Question 3

Which formula correctly represents the calculation of the correlation coefficient $$r$$ for two variables $$X$$ and $$Y$$?

Accepted Answer

$$ r = \frac{\sum (X_i - \bar{X})(Y_i - \bar{Y})}{\sqrt{\sum (X_i - \bar{X})^2$ \sum (Y_i - \bar{Y})^2$}} $$

Question 4

Which of the following is NOT an assumption of linear regression?

Accepted Answer

The explanatory variable must be categorical.

Question 5

A researcher fits a linear regression model and obtains the equation $$ \hat{y} = 2 + 3x . $$What is the predicted value of $$y$$ when $$x = 4$$?

Accepted Answer

$$ \hat{y} = 14 $$

Question 6

Which of the following best describes the concept of leverage in regression analysis?

Accepted Answer

A data point that is far from the mean of the explanatory variable and can strongly influence the regression line.

Question 7

Given the regression equation $$ \hat{y} = 5 - 0.5x $$, what is the residual for an observed value $$x = 6$$, $$y = 1$$?

Accepted Answer

$$ -1 $$

Question 8

Which sampling method divides the population into groups and then randomly selects some groups to sample all members within those groups?

Accepted Answer

Cluster sampling

Question 9

A pharmaceutical company wants to test a new drug. They randomly assign patients to receive either the drug or a placebo. What is the purpose of the placebo group?

Accepted Answer

To control for the psychological effects of receiving a treatment.

Question 10

Which of the following statements about statistically significant results is correct?

Accepted Answer

Statistically significant means the observed effect is unlikely to have occurred by chance, given a pre-specified significance level.

Question 11

Which sampling method is most likely to introduce bias if only volunteers participate?

Accepted Answer

Voluntary response sampling

Question 12

In an experiment, what is the difference between a factor and a treatment?

Accepted Answer

A factor is a variable manipulated by the experimenter, while a treatment is a specific combination of factor levels applied to subjects.

Question 13

Which of the following is an example of a lurking variable in a study examining the relationship between exercise and weight loss?

Accepted Answer

Diet of the participants

Question 14

A researcher uses systematic sampling to select every 10th person from a list of 1,000. How many people will be in the sample?

Accepted Answer

100

Question 15

Which of the following best describes the placebo effect?

Accepted Answer

The effect observed in subjects who believe they are receiving treatment, even if they are not.

Question 16

In regression analysis, what does the term 'variation' refer to?

Accepted Answer

The spread of the data points around the mean, often measured by variance or standard deviation.

Question 17

Which sampling method is most appropriate for ensuring that all subgroups of a population are represented proportionally?

Accepted Answer

Stratified sampling

Question 18

A study finds a correlation coefficient $$ r = -0.85 $$ between hours spent watching TV and exam scores. What does this indicate?

Accepted Answer

A strong negative linear relationship.

Question 19

Which of the following is NOT a type of bias in sampling?

Accepted Answer

Random sampling bias

Statistics Study Guide: Regression, Sampling, and Experimental Design

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