What are the implications of having a small expected frequency in a Chi-square test for goodness of fit?
- It can cause the Chi-square distribution approximation to be inaccurate
- It increases the degrees of freedom
- It leads to a higher power of the test
- It leads to a smaller Chi-square statistic
If the expected frequency in any category is too small (common rule of thumb is less than 5), the Chi-square distribution approximation may be inaccurate, leading to incorrect conclusions.
If the calculated Chi-square statistic is greater than the critical Chi-square value, we ________ the null hypothesis.
- accept
- adjust
- reject
- retain
If the calculated Chi-square statistic is greater than the critical Chi-square value (based on the chosen significance level and the degrees of freedom), we reject the null hypothesis. This means the observed distribution significantly differs from the expected distribution.
Factor analysis reduces the dimensions of data by combining similar _______ into groups or factors.
- eigenvalues
- factors
- observations
- variables
Factor analysis reduces the dimensions of data by combining similar variables into groups or factors.
The ________ distribution is symmetric and its mean, median and mode are equal.
- Binomial
- Normal
- Poisson
- Uniform
The normal distribution, also known as the Gaussian distribution, is symmetric, and its mean, median, and mode are all equal. It is shaped like a bell curve, with the data evenly distributed about the mean.
What are the key assumptions for applying the Sign Test?
- Data must be at least ordinal
- Data must be categorical
- Data must be continuous
- Data must be normally distributed
The key assumption for applying the Sign Test is that the data must be at least ordinal. The Sign Test is a non-parametric test and does not require the assumption of normality.
The Sign Test is based on the direction of the _________ between pairs.
- differences
- medians
- ranks
- signs
The Sign Test is based on the direction of the differences between pairs.
What techniques can be used to detect multicollinearity in a multiple regression model?
- Analysis of Variance (ANOVA)
- Chi-square test
- T-test
- Variance Inflation Factor (VIF)
The Variance Inflation Factor (VIF) is commonly used to detect multicollinearity in regression analysis.
What is the probability of an event that is certain to happen?
- 0
- 0.5
- 1
- The probability is undefined for certain events
The probability of an event that is certain to happen is 1. This is based on the definition of probability as a measure that takes values between 0 and 1, inclusive. An event with a probability of 1 is a sure event.
The optimal number of clusters in K-means clustering is often determined using the ________ method.
- elbow
- foot
- hand
- knee
The optimal number of clusters in K-means clustering is often determined using the elbow method. This involves plotting the explained variation as a function of the number of clusters and picking the elbow of the curve as the number of clusters to use.
The _______ test compares the means of two independent groups.
- Chi-square
- Independent t
- Paired t
- Z
An Independent t-test (or two sample t-test) compares the means of two independent groups.