A _______ test is used when the population variance is known.
- Chi-square
- F
- T
- Z
A Z-test is used when the population variance is known. It's based on the standard normal distribution.
The closer the correlation coefficient is to __ or __, the stronger the correlation.
- -1 or 1
- 0
- 0.5 or -0.5
- 1 or 2
The correlation coefficient measures the strength and direction of a linear relationship between two variables. It ranges from -1 to 1, with -1 indicating a perfect negative correlation, 1 indicating a perfect positive correlation, and 0 indicating no correlation. Thus, the closer the correlation coefficient is to -1 or 1, the stronger the correlation.
The number of trials in a binomial distribution is ________, whereas in a Poisson distribution, it's theoretically infinite.
- dependent on the sample size
- dependent on the success rate
- fixed
- infinite
In a binomial distribution, the number of trials is fixed (a fixed number of independent trials are considered), whereas in a Poisson distribution, theoretically, an infinite number of events can occur.
How do non-parametric statistical methods deal with outliers compared to parametric methods?
- They are more robust to outliers
- They are more sensitive to outliers
- They don't handle outliers
- They eliminate outliers before analysis
Non-parametric statistical methods are more robust to outliers compared to parametric methods. This is because non-parametric tests often use medians and ranks, which are less sensitive to extreme values, compared to means which are used in parametric tests.
How does the concept of geometric mean differ from the arithmetic mean?
- Geometric mean cannot be used for negative numbers, arithmetic mean can
- Geometric mean uses addition, arithmetic mean uses multiplication
- Geometric mean uses multiplication, arithmetic mean uses addition
- There is no difference
The arithmetic mean involves the sum of the values divided by the number of values, while the geometric mean involves multiplying all the values together, and then taking the nth root of the product (where n is the total number of values). Geometric mean is especially useful when comparing different items with extremely variable ranges.
What are some real-world implications of kurtosis in a dataset?
- Datasets with high kurtosis are easier to interpret
- High kurtosis can indicate a bias in data collection
- High kurtosis can indicate the presence of outliers
- Kurtosis does not have real-world implications
In real-world data analysis, kurtosis is used to identify the presence of outliers. High kurtosis in a dataset may signal an increase in tail risk. This is particularly relevant in fields like finance, where tail risk could translate into heavier losses than the normal distribution would predict.
What does the Wilcoxon Signed Rank Test compare in paired samples?
- Means
- Medians
- Modes
- Variance
The Wilcoxon Signed Rank Test compares the medians in paired samples.
What is the difference between correlation and causation?
- Causation implies correlation
- Correlation and causation are independent of each other
- Correlation implies causation
- Correlation means there is no causation
While correlation simply implies a relationship between two variables, causation goes a step further to explain that one variable actually causes the other to change. It's important to remember that correlation does not imply causation. However, if there is causation, there's likely to be correlation.
The correlation coefficient is denoted by the letter __.
- C
- P
- R
- S
The correlation coefficient is often denoted by the letter 'R'. In the case of Pearson's correlation, it's specifically denoted as 'r'. It measures the degree of relationship between two variables.
________ data is data that can be organized or ranked in a specific order.
- Continuous
- Discrete
- Nominal
- Ordinal
Ordinal data is a type of categorical data that can be organized or ranked in a specific order. For example, customer satisfaction ratings (satisfied, neutral, dissatisfied) can be organized from most to least satisfied.