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.
How does a higher R-squared value impact the inference in multiple linear regression?
- It decreases the number of observations
- It improves the interpretability of the model
- It increases the residuals
- It makes the model more complex
The R-squared value measures the proportion of the variance in the dependent variable that is predictable from the independent variables. A higher R-squared value, closer to 1, implies a higher proportion of variability in the response variable is explained by the predictors, improving the model's interpretability and predictive power.
In multiple linear regression, the __________ test is used to test if a group of variables contributes to the prediction of the response.
- Chi-square test
- F-test
- T-test
- Z-test
The F-test is used in multiple regression to test whether at least one of the predictors' regression coefficient is not equal to zero. In other words, it tests whether the predictors are significant in explaining the response variable.
How does the sample size relate to the power of a test?
- It depends on the effect size
- Larger sample sizes decrease power
- Larger sample sizes increase power
- Sample size has no influence on power
Larger sample sizes increase the power of a test because they provide more data, reducing the influence of random error and making it easier to detect an effect if one exists. This is why researchers often aim to recruit as large a sample as possible, within the constraints of their resources.
If two events A and B are mutually exclusive, the probability of both occurring is _______.
- 0
- 0.5
- 1
- The probability is undefined
If two events A and B are mutually exclusive, the probability of both occurring is 0. Mutually exclusive events cannot occur at the same time.
How does the Law of Large Numbers impact the calculation of probabilities?
- It changes the probability of an event based on previous outcomes.
- It doesn't affect the calculation of probabilities.
- It guarantees that the experimental probability gets closer to the theoretical probability as the number of trials increases.
- It states that all probabilities must be equal.
The Law of Large Numbers impacts the calculation of probabilities by asserting that as the number of trials (or observations) increases, the experimental probabilities will get closer and closer to the theoretical (or true) probabilities. It gives validity to the notion of probability in practical applications.