How is a probability distribution defined?
- It is the average value of a dataset
- It is the highest and lowest value of a dataset
- It is the likelihood of each possible outcome of a random variable
- It is the spread of possible values in a dataset
A probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment. For a random variable, the probability distribution is the probability that the variable takes a particular value.
What does a Principal Component represent in a dataset?
- A combination of original features
- A feature of the dataset
- A group of similar data points
- A target variable
A Principal Component is a linear combination of the original features in a dataset. Each principal component is orthogonal to each other, meaning they are uncorrelated and each represents a different direction in which the data varies.
Can the Mann-Whitney U test be used for paired samples?
- No
- Only if the data is normally distributed
- Only if the variances are equal
- Yes
No, the Mann-Whitney U test is not used for paired samples. It is designed for two independent samples. For paired samples, a different test, such as the Wilcoxon signed-rank test, would be more appropriate.
When is it more appropriate to use the Mann-Whitney U test than a t-test?
- When data is normally distributed
- When data is not normally distributed
- When sample sizes are equal
- When the variances of the two groups are equal
The Mann-Whitney U test is more appropriate to use than a t-test when the data is not normally distributed. This test is a non-parametric alternative to the independent t-test and does not assume normality.
In the Kruskal-Wallis Test, if the p-value is less than the chosen significance level, we ________ the null hypothesis.
- accept
- consider
- ignore
- reject
If the p-value is less than the chosen significance level in the Kruskal-Wallis Test, we reject the null hypothesis. It means there is enough evidence to suggest that at least one of the groups is different from the others.
In what type of data distribution is the mean usually greater than the median?
- Negatively skewed distribution
- Normal distribution
- Positively skewed distribution
- Uniform distribution
In a positively skewed distribution, the mean is usually greater than the median. A positive skew means the right tail of the distribution is longer or fatter. The mean, being affected by the values of the data points, gets dragged in the direction of the tail, and hence is typically greater than the median in a positively skewed distribution.
A distribution that is symmetric and bell-shaped is known as a _______ distribution.
- Bimodal
- Normal
- Skewed
- Uniform
A normal distribution, also known as Gaussian distribution, is symmetric and bell-shaped. It is characterized by its mean and standard deviation. The mean, mode and median are all equal and are located at the center of the distribution.
Data that can be divided into categories but has no order or priority is known as ________ data.
- Continuous
- Discrete
- Nominal
- Ordinal
Nominal data is data that can be divided into categories but has no order or priority. It is a type of categorical data that simply allows us to classify or categorize. Examples include types of cuisine (Italian, Chinese, Mexican, etc.), hair color, or city of residence.
When two events are mutually exclusive, what is the probability that both will occur?
- 0
- 0.5
- 1
- The sum of the probabilities of the two events
When two events are mutually exclusive, it means they cannot occur at the same time. Therefore, the probability that both will occur is 0.
The ___________ correlation is a non-parametric measure of correlation based on data rank.
- Kendall's
- Pearson's
- Point-biserial
- Spearman's
Spearman's correlation is a non-parametric measure of rank correlation. It assesses how well the relationship between two variables can be described using a monotonic function. This makes it suitable for both continuous and discrete ordinal variables.