In what situations is the coefficient of variation a better measure of dispersion than the standard deviation?
- When data sets have different units
- When data sets have the same units
- When the data set is normally distributed
- When the mean of the data set is zero
The coefficient of variation (CV) is a standardized measure of dispersion that is unitless. It's particularly useful when comparing the dispersion of two or more datasets that have different units or significantly different means. Standard deviation, on the other hand, has the same units as the data, which may not be helpful for comparisons across different datasets.
Under what circumstances can the conditional probability of an event be equal to its marginal probability?
- When the event is certain
- When the event is dependent on all other events
- When the event is impossible
- When the event is independent of all other events
The conditional probability of an event A given an event B equals the marginal probability of A when A and B are independent. This is because the occurrence of B does not change the probability of A if they are independent.
What type of data is the Mann-Whitney U test used for?
- Interval data
- Nominal data
- Ordinal data
- Ratio data
The Mann-Whitney U test is used for ordinal data, which can be ranked but have unknown or non-equivalent differences between values. It can also be used with interval and ratio data that do not meet the assumptions of other tests.
What does the 'mode' refer to in a data set?
- The average value
- The middle value
- The most frequently occurring value
- The range of values
The mode in a data set refers to the most frequently occurring value. In a dataset, the mode is the value that appears the most number of times. A dataset may have one mode (unimodal), two modes (bimodal), or multiple modes (multimodal).
How is the Chi-square statistic calculated in a goodness of fit test?
- The differences between observed and expected frequencies are averaged
- The differences between observed and expected frequencies are divided by the expected frequencies
- The differences between observed and expected frequencies are squared and summed
- The differences between observed and expected frequencies are squared, summed, and then the square root is taken
In a Chi-square goodness of fit test, the Chi-square statistic is calculated by squaring the differences between observed and expected frequencies, then summing these squared differences.
In a ________ distribution, the events occur with a known constant mean rate and independently of the time since the last event.
- Binomial
- Normal
- Poisson
- Uniform
The Poisson distribution models the number of events happening in a fixed interval of time or space, given a constant mean rate of occurrence and independence of the time since the last event.
Multicollinearity refers to a situation where two or more _______ are highly linearly related.
- constants
- predictors
- residuals
- responses
Multicollinearity occurs when two or more predictor variables in a multiple regression are highly correlated with each other.
How does the confidence level of an interval influence the width of that interval?
- Higher confidence level leads to a narrower interval
- Higher confidence level leads to a wider interval
- Higher confidence level makes the interval skewed
- It does not influence the width
The higher the confidence level, the wider the interval. This is because to be more confident that we've captured the true population parameter, we need to provide a wider range of possible values.
In the context of Bayes' theorem, the probability of the data given a specific event is called the ________.
- joint
- likelihood
- marginal
- prior
The likelihood is the probability of the data given a specific event. It is part of Bayes' theorem, which is used to update the probability of a hypothesis based on new data.
What does a positive Spearman's rank correlation coefficient mean?
- One variable increases as the other decreases
- One variable is twice as large as the other
- Variables decrease together
- Variables increase together
A positive Spearman's rank correlation coefficient indicates that as one variable increases, the other also increases. This suggests a positive association between the variables.