What is the impact of a large sample size on the confidence interval of the mean?
- Larger sample size has no impact on the confidence interval
- Larger sample size leads to a narrower interval
- Larger sample size leads to a wider interval
- Larger sample size makes the interval skewed
Larger sample sizes lead to narrower confidence intervals. With more data, we're able to estimate the population parameter more precisely, thus the range of values within which we believe the parameter lies (the confidence interval) gets smaller.
Spearman's Rank Correlation is used when the variables are measured on a ________ scale.
- Interval
- Nominal
- Ordinal
- Ratio
Spearman's Rank Correlation is used when the variables are measured on an ordinal scale, as it compares the ranks of data. It can also be used with interval and ratio scales, particularly when a non-parametric measure of association is desired.
What are the assumptions of the Mann-Whitney U test?
- Equal variances and independent observations
- Independent observations and normally distributed residuals
- Independent observations and similarly shaped distributions
- Normal distribution, equal variances, and independent observations
The assumptions of the Mann-Whitney U test are that observations are independent and that the distributions are similarly shaped. It does not require the assumption of normal distribution or equal variances.
If the null hypothesis is false, but we fail to reject it, what type of error have we made?
- Both Type I and Type II error
- Neither Type I nor Type II error
- Type I error
- Type II error
If the null hypothesis is false, but we fail to reject it, we have made a Type II error. This is also known as a "false negative" result.
When two variables increase and decrease together, they are said to have a ________ correlation.
- negative
- positive
- strong
- zero
When two variables increase and decrease together, they are said to have a positive correlation. This is indicated by a positive Pearson's Correlation Coefficient.
The Kruskal-Wallis Test ranks all the data from all groups together; it then tests whether the ________ ranks differ significantly between the groups.
- average
- mean
- median
- mode
The Kruskal-Wallis Test ranks all the data from all groups together; it then tests whether the mean ranks differ significantly between the groups.
A statistical technique that uses several explanatory variables to predict the outcome of a response variable is called ________.
- ANOVA
- correlation
- multiple linear regression
- simple linear regression
Multiple linear regression is a statistical technique used to predict the outcome of a response variable based on the value of two or more explanatory variables.
When two or more independent variables in a regression model are highly correlated, it's known as ________.
- Collinearity
- Interaction
- Multicollinearity
- Overfitting
This is known as multicollinearity. In regression analysis, multicollinearity refers to a situation where two or more independent variables are highly correlated. This can make it difficult to determine the effect of each individual variable on the dependent variable and can lead to unstable and unreliable estimates.
The ________ of a distribution is the point of maximum frequency.
- Mean
- Median
- Mode
- Standard deviation
The mode of a distribution is the point of maximum frequency. It represents the value that appears most frequently in a data set. A distribution can be unimodal (one mode), bimodal (two modes), or multimodal (more than two modes).
How can you identify the presence of bimodal distribution in data?
- By looking at the mean and median
- By looking at the skewness
- By looking at the standard deviation
- By looking for two peaks in a histogram
A bimodal distribution is one that has two different modes, or peaks. This can often be identified in a histogram, where two separate areas of the data have higher frequencies. This might indicate that the data is drawn from two different populations.
When adding polynomial terms or interaction effects, what key assumption of regression might be violated?
- Homoscedasticity
- Independence of observations
- Linearity
- Normality of errors
When adding polynomial terms or interaction effects to a regression model, the assumption of linearity might be violated. The linearity assumption in regression analysis states that the relationship between the independent and dependent variables is linear, i.e., a change in the independent variable will result in a constant change in the dependent variable. When adding polynomial terms or interaction effects, we are essentially modeling a non-linear relationship.
In probability, an ________ is the set of possible results of an experiment.
- Event
- Outcome
- Probability Space
- Sample Space
In probability theory, an "outcome" is a possible result of an experiment or trial. For example, if you toss a coin, the possible outcomes are heads or tails. Each outcome of an experiment corresponds to a unique event.