You're playing a game where you flip a coin. Heads, you win $10. Tails, you lose $5. What is the expected value of playing this game?
$2.50
$0.00
$5.00
-$2.50
Let X be a random variable representing the number of heads when you toss a fair coin three times. What is the variance of X?
1
0.5
0.75
1.5
Which component of a time series reflects long-term changes in the data over time?
Irregularity
Trend
Cyclical Variation
Seasonality
A random variable follows a uniform distribution between 0 and 10. What is the probability that the variable takes a value between 3 and 7?
0.4
0.3
0.7
The number of cars passing a certain point on a highway averages 10 per hour. What is the probability that exactly 15 cars pass that point in a given hour?
0.0347
0.25
0.15
A 95% confidence interval for a population mean is calculated to be (60, 80). What is the correct interpretation of this interval?
If we were to repeatedly construct confidence intervals using this method, 95% of them would contain the true population mean.
There is a 95% probability that the true population mean falls between 60 and 80.
If we were to repeatedly sample from this population, 95% of the time the sample mean would fall between 60 and 80.
We are 95% confident that the sample mean falls between 60 and 80.
What is the range of possible values for the coefficient of determination (R²)?
0 to 1
-∞ to +∞
-1 to 1
Depends on the data
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.
What is the purpose of calculating a correlation coefficient?
To determine the cause-and-effect relationship between two variables.
To test the significance of the difference between two means.
To measure the strength and direction of the linear relationship between two variables.
To predict the value of one variable based on the value of another variable.
A high R² value in a regression analysis always indicates a good fit of the model. Is this statement true or false?
True
False