What is the primary purpose of inferential statistics?
To organize and clean raw data.
To make generalizations about a population based on a sample.
To visually represent data using graphs and charts.
To describe and summarize data.
What is the range of possible values for the coefficient of determination (R²)?
-1 to 1
-∞ to +∞
0 to 1
Depends on the data
Suppose 60% of emails in your inbox are spam and 40% are legitimate. Also, 95% of spam emails contain the word 'free,' while only 1% of legitimate emails do. If an email contains the word 'free,' what's the probability it's spam?
0.996
0.004
0.57
0.05
What does a residual in regression analysis represent?
The slope of the regression line
The difference between the observed value and the predicted value of the dependent variable
The intercept of the regression line
The correlation between the independent and dependent variables
What does an R-squared value of 0.80 indicate?
The correlation between the variables is 0.80.
80% of the variation in the dependent variable is explained by the independent variable.
20% of the variation in the dependent variable is explained by the independent variable.
The slope of the regression line is 0.80.
When would you use a paired t-test instead of an independent t-test?
When comparing the means of two groups with unequal variances.
When comparing the means of three or more groups.
When comparing the means of two independent groups.
When comparing the means of the same group before and after a treatment.
A coin is flipped 5 times. What is the probability of getting exactly 3 heads?
0.5
0.6875
0.3125
0.25
A high R² value in a regression analysis always indicates a good fit of the model. Is this statement true or false?
False
True
A researcher wants to determine if a new drug reduces blood pressure more effectively than a placebo. They measure the blood pressure of the same group of patients before and after taking the drug and placebo (in random order). What test should they use?
One-sample t-test
Independent samples t-test
ANOVA
Paired t-test
In simple linear regression, what does a negative slope of the regression line indicate?
There is no relationship between the independent and dependent variables.
As the independent variable increases, the dependent variable increases.
As the independent variable increases, the dependent variable decreases.
The relationship between the independent and dependent variables is non-linear.