What type of correlation does the Spearman's Rank Correlation test measure?
- Correlation of variances
- Linear correlation
- Monotonic correlation
- Polynomial correlation
Spearman's Rank Correlation test measures monotonic correlation, which indicates whether an increase in one variable will increase or decrease the other variable. It does not require the relationship between the variables to be linear.
The _______ of a confidence interval corresponds to the total area under the curve that is excluded on both sides of the curve.
- Confidence level
- Margin of error
- Population parameter
- Standard error
The margin of error of a confidence interval corresponds to the total area under the curve that is excluded on both sides of the curve. This margin of error determines the width of the confidence interval.
What happens if the assumption of homoscedasticity is violated in simple linear regression?
- It has no effect on the regression model
- It makes the regression model more accurate
- It makes the regression model perfectly fit the data
- It makes the standard errors and confidence intervals invalid
Homoscedasticity is the assumption that the variance of the residuals is constant across all levels of the independent variable. If this assumption is violated (a condition known as heteroscedasticity), it can lead to unreliable and inefficient estimates of the standard errors. This, in turn, can make the confidence intervals and hypothesis tests invalid.
In the context of a continuous random variable, the ________ function gives the probability that the variable takes a value less than or equal to a certain value.
- Cumulative Distribution Function
- Probability Density Function
- Probability Mass Function
- Random Function
The Cumulative Distribution Function (CDF) of a random variable is defined as the probability that the variable takes a value less than or equal to a certain value. The difference between discrete and continuous random variables is the way their probabilities are assigned.
The ________ is the most frequent value in a data set.
- Mean
- Median
- Mode
- nan
The mode is the value that appears most frequently in a data set. A set of data may have one mode, more than one mode, or no mode at all.
If the p-value in a Chi-square test is less than the significance level, we ________ the null hypothesis.
- accept
- ignore
- question
- reject
If the p-value in a Chi-square test is less than the chosen significance level, we reject the null hypothesis. This means that we have enough evidence to conclude that the two variables are not independent.
How can Bayes' theorem be applied to hypothesis testing?
- All of the above
- It can't be used in hypothesis testing
- It is used to calculate the probability of the null hypothesis given the data
- It is used to reject or fail to reject the null hypothesis
Bayes' theorem can be applied to hypothesis testing by calculating the probability of the hypothesis given the observed data. This differs from traditional frequentist hypothesis testing, where the data is assumed given and the hypothesis is tested.
How does kurtosis affect the tails of a distribution?
- Changes the skewness
- Has no effect
- Makes the tails fatter
- Makes the tails thinner
Kurtosis is a statistical measure that defines how heavily the tails of a distribution differ from the tails of a normal distribution. In other words, kurtosis identifies whether the tails of a given distribution contain extreme values. Positive kurtosis indicates a distribution with tails or outliers that are fatter and more extreme than a normal distribution.
Descriptive statistics summarizes and interprets the ________ of a dataset.
- characteristics
- outliers
- population
- sample
Descriptive statistics summarizes and interprets the characteristics of a dataset. These characteristics can include measures of central tendency like mean, median, and mode, measures of dispersion like range, variance, and standard deviation, and measures of shape like skewness and kurtosis. This branch of statistics provides a summary about the samples and the measures that have been made. It's essentially a way to describe and summarize the data.
What is the range of a discrete random variable?
- All negative numbers
- All positive numbers
- All real numbers
- The set of all possible outcomes
The range of a discrete random variable is the set of all possible outcomes or values that the variable can take.