In a normal distribution, about 95% of the data lies within _______ standard deviations of the mean.
- Four
- One
- Three
- Two
According to the empirical rule (also known as the 68-95-99.7 rule), in a normal distribution, about 68% of the data lies within one standard deviation of the mean, about 95% lies within two standard deviations, and about 99.7% lies within three standard deviations.
How do you diagnose multicollinearity in a multiple linear regression model?
- By calculating the R-squared value
- By checking the correlation matrix and Variance Inflation Factor (VIF)
- By looking at the residual plot
- By looking at the scatter plot
Multicollinearity is diagnosed in a multiple linear regression model by checking the correlation matrix and the Variance Inflation Factor (VIF). A high correlation between independent variables and a VIF greater than 5 or 10 suggests the presence of multicollinearity.
How can transformations help in reducing skewness in a dataset?
- They can make the distribution more symmetric
- They can shift the mean towards the skew
- They can shift the mode towards the skew
- Transformations cannot reduce skewness
Transformations, such as logarithmic or square root transformations, can help in reducing skewness by making the distribution more symmetric. The choice of transformation often depends on the degree and direction of skewness.
How does the standard deviation affect the shape of a normal distribution?
- Changes the kurtosis
- Changes the skewness
- Changes the spread or dispersion
- Does not affect the shape
The standard deviation, a measure of dispersion or spread, determines the width of a normal distribution. A larger standard deviation results in a wider, flatter distribution, while a smaller standard deviation results in a narrower, steeper distribution.
A _______ t-test is used to compare two related samples or repeated measurements on a single sample.
- Independent
- One-sample
- Paired
- Two-sample
A Paired t-test is used to compare two related samples or repeated measurements on a single sample. It's often used in before-and-after scenarios where the same individuals are measured twice.
What is a random variable in probability theory?
- A factor that doesn't change
- A variable that can take on different values, each with an associated probability
- An unknown variable
- An unpredictable factor
A random variable in probability theory is a variable that can take on different values, each with an associated probability. It's not "random" in the everyday sense of the word, but its exact value is uncertain until it's observed.
The _________ test is a non-parametric test that compares the medians of two paired groups.
- Chi-square
- Mann-Whitney U
- Sign
- Wilcoxon Signed Rank
The Wilcoxon Signed Rank test is a non-parametric test that compares the medians of two paired groups.
Why is interval estimation generally preferred over point estimation?
- Because it gives more accurate results
- Because it is easier to calculate
- Because it is less affected by outliers
- Because it provides a range of possible values rather than a single point
Interval estimation is generally preferred over point estimation because it provides a range of possible values rather than a single value. This range of values gives a better understanding of the uncertainty around the estimate, hence, it provides more information than a single point estimate.
Spearman's Rank Correlation is especially useful when the relationship between variables is ________, but not necessarily linear.
- Bimodal
- Monotonic
- Negative
- Positive
Spearman's Rank Correlation is especially useful when the relationship between variables is monotonic, but not necessarily linear. A monotonic relationship is one where the variables tend to change together, but not necessarily at a constant rate.
If the null hypothesis is true in ANOVA, the F-statistic follows a ________ distribution.
- Binomial
- Chi-Square
- F
- Normal
In ANOVA, if the null hypothesis is true, the F-statistic follows an F-distribution. The F-distribution is a probability distribution that is used most commonly in Analysis of Variance.