The _______ test compares the means of two independent groups.
- Chi-square
- Independent t
- Paired t
- Z
An Independent t-test (or two sample t-test) compares the means of two independent groups.
How does a higher R-squared value impact the inference in multiple linear regression?
- It decreases the number of observations
- It improves the interpretability of the model
- It increases the residuals
- It makes the model more complex
The R-squared value measures the proportion of the variance in the dependent variable that is predictable from the independent variables. A higher R-squared value, closer to 1, implies a higher proportion of variability in the response variable is explained by the predictors, improving the model's interpretability and predictive power.
In multiple linear regression, the __________ test is used to test if a group of variables contributes to the prediction of the response.
- Chi-square test
- F-test
- T-test
- Z-test
The F-test is used in multiple regression to test whether at least one of the predictors' regression coefficient is not equal to zero. In other words, it tests whether the predictors are significant in explaining the response variable.
How does the sample size relate to the power of a test?
- It depends on the effect size
- Larger sample sizes decrease power
- Larger sample sizes increase power
- Sample size has no influence on power
Larger sample sizes increase the power of a test because they provide more data, reducing the influence of random error and making it easier to detect an effect if one exists. This is why researchers often aim to recruit as large a sample as possible, within the constraints of their resources.
If two events A and B are mutually exclusive, the probability of both occurring is _______.
- 0
- 0.5
- 1
- The probability is undefined
If two events A and B are mutually exclusive, the probability of both occurring is 0. Mutually exclusive events cannot occur at the same time.
How does the Law of Large Numbers impact the calculation of probabilities?
- It changes the probability of an event based on previous outcomes.
- It doesn't affect the calculation of probabilities.
- It guarantees that the experimental probability gets closer to the theoretical probability as the number of trials increases.
- It states that all probabilities must be equal.
The Law of Large Numbers impacts the calculation of probabilities by asserting that as the number of trials (or observations) increases, the experimental probabilities will get closer and closer to the theoretical (or true) probabilities. It gives validity to the notion of probability in practical applications.
The Sign Test is based on the direction of the _________ between pairs.
- differences
- medians
- ranks
- signs
The Sign Test is based on the direction of the differences between pairs.
What is the null hypothesis in an ANOVA test?
- The means of all groups are different
- The means of all groups are equal
- The variances of all groups are different
- The variances of all groups are equal
The null hypothesis in an ANOVA test is that the means of all groups are equal. If the p-value obtained from the ANOVA test is less than the significance level, the null hypothesis is rejected, implying that there is a significant difference between at least two of the group means.
A distribution with a positive ________ has a long tail in the positive direction.
- Kurtosis
- Mean
- Median
- Skewness
A distribution with positive skewness is said to be positively skewed or right-skewed, which means it has a long tail in the positive direction on the number line.
What is the key difference between a discrete and a continuous random variable?
- Discrete variables are predictable, continuous variables are not
- Discrete variables can only take on a countable number of values, continuous variables can take on any value within a certain range
- Discrete variables can take on any value, continuous variables can take on only integer values
- There's no difference between discrete and continuous random variables
Discrete random variables are variables that can only take on a countable number of values, such as integers, while continuous random variables can take on any value within a certain range or interval.