A histogram with two peaks is known as a ________ distribution.

  • Bimodal
  • Multimodal
  • Normal
  • Uniform
A histogram with two distinct peaks is referred to as a bimodal distribution. This might suggest that the data contains two different groups, each with their own mode, or most common value.

In Bayes' theorem, what does the prior probability represent?

  • The likelihood of the evidence
  • The probability of an event before evidence is observed
  • The probability of the evidence given the event
  • The updated probability after evidence is observed
The prior probability in Bayes' Theorem is the initial or original probability of an event before new evidence is taken into account. It represents our initial belief about the event.

The Chi-square test for goodness of fit tests the hypothesis that the observed distribution follows a ________ distribution.

  • expected
  • normal
  • skewed
  • uniform
The Chi-square test for goodness of fit is used to determine whether the observed distribution of data follows an expected distribution.

How does PCA relate to the Singular Value Decomposition (SVD) technique?

  • PCA can be implemented using SVD
  • SVD is a prerequisite for PCA
  • SVD is a type of PCA
  • They are entirely different techniques
PCA can be implemented using SVD. Both techniques can be used for dimensionality reduction, and they both rely on eigenvalue decomposition, but SVD decomposes the data matrix directly, while PCA works on the covariance matrix of the data.

A wider confidence interval indicates a higher level of _______ about the estimate.

  • Certainty
  • Standard deviation
  • Uncertainty
  • Variance
A wider confidence interval suggests a higher level of uncertainty about the estimate because the range of values for the population parameter is larger.

In multiple linear regression, what does each coefficient represent?

  • The average change in the dependent variable for one unit of change in the independent variable, holding all other independent variables constant
  • The correlation between the dependent variable and the independent variable
  • The error term in the regression model
  • The total variation in the dependent variable explained by the independent variable
In multiple linear regression, each coefficient represents the average change in the dependent variable for one unit of change in the independent variable, while holding all other independent variables constant.

How is the Bartlett's Test of Sphericity used in factor analysis?

  • It tests the assumption of equal variances
  • It tests the assumption of linearity
  • It tests the assumption of normality
  • It tests the assumption that the variables are uncorrelated
Bartlett's Test of Sphericity is used in factor analysis to test the hypothesis that the variables are uncorrelated in the population. In other words, the population correlation matrix is an identity matrix. A significant test indicates that a factor analysis may be useful with your data.

A __________ is a graphical representation used to observe and show relationships between two numeric variables.

  • Bar chart
  • Histogram
  • Pie chart
  • Scatter plot
A scatter plot is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data. It's used to observe and show the relationship between two numeric variables.

What is the relationship between the probability of a Type I error and the significance level of a test?

  • It depends on the sample size
  • There is no relationship
  • They are directly proportional
  • They are inversely proportional
The probability of a Type I error (false positive) is the same as the significance level of a test. A significance level of 0.05, for instance, means there's a 5% chance of rejecting a true null hypothesis (Type I error).

What is the concept of the standard error in relation to a sampling distribution?

  • It is the mean of the population
  • It is the mean of the sampling distribution
  • It is the standard deviation of the population
  • It is the standard deviation of the sampling distribution
The standard error is a statistical term that measures the standard deviation of the sampling distribution. In other words, it provides a measure of the variability or dispersion of sample means around the population mean. A smaller standard error indicates that the sample mean is likely to be a closer approximation to the population mean.

If the assumptions of a parametric test are violated, it might be appropriate to use a ________ statistical method.

  • biased
  • non-parametric
  • normal
  • parametric
If the assumptions of a parametric test are violated, it might be appropriate to use a non-parametric statistical method. Non-parametric methods have fewer assumptions and can be used with different types of data.

What is a key difference between parametric and non-parametric statistical methods?

  • The amount of data they can handle
  • The assumptions they make about the data distribution
  • The speed at which they analyze data
  • The type of variables they can analyze
The key difference between parametric and non-parametric statistical methods is the assumptions they make about the data distribution. Parametric methods assume that the data follow a certain distribution, while non-parametric methods do not make these assumptions.