Why is it important to consider the power of a test when designing a study?
- To ensure the study can detect an effect if it exists
- To ensure the study does not detect an effect if it does not exist
- To maximize the chance of a Type I error
- To minimize the chance of a Type I error
The power of a test is the ability of the test to detect an effect if it truly exists. It's the probability that the test correctly rejects a false null hypothesis. High power is desirable because it means the test is less likely to make a Type II error (false negative). When designing a study, it's important to choose a sample size and significance level that will provide enough power to detect an effect if one exists.
_______ is a measure of how spread out the numbers in a dataset are around the mean.
- Median
- Range
- Standard Deviation
- Variance
Standard deviation is a measure of how spread out the numbers in a dataset are around the mean. It measures the average distance between each data point and the mean. The higher the standard deviation, the more spread out the data is.
In the context of cluster analysis, what is the 'centroid'?
- The average distance between clusters
- The geometric center of a cluster
- The largest point in a cluster
- The smallest point in a cluster
The centroid is the geometric center of a cluster. In other words, it's the mean value of all the points in a specific cluster.
Which measure of central tendency is most affected by extreme values or outliers?
- All are equally affected
- Mean
- Median
- Mode
The mean is most affected by extreme values or outliers. The mean calculates the average of all data points in a dataset. Therefore, when an extreme value (either very high or very low compared to the rest) is introduced, it can significantly impact the mean. The median and mode are less affected by outliers.
How does the Sign Test handle ties between paired samples?
- Ties are averaged
- Ties are counted as half a sign
- Ties are discarded
- Ties are included in the test
In the Sign Test, ties between paired samples are generally discarded and not included in the final calculation.
Which type of test is the Sign Test: parametric or non-parametric?
- Both
- Non-parametric
- Parametric
- nan
The Sign Test is a non-parametric test used to test the median of a distribution, or to compare the medians of two distributions.
What does the term 'population' mean in the context of statistics?
- All animals in a zoo
- All people in a country
- The entire group that you are interested in studying
- The group of people who respond to a survey
In the context of statistics, a 'population' refers to the entire set of individuals or items that we are interested in studying. This could range from all the people living in a country, to all the particles in a chemical solution, to all the sales transactions in a store, and so forth. When we collect data from every individual or item in the population, it's called a census. The information gained from a population is reliable and accurate because it accounts for everyone or everything we want to study.
What is an event in the context of probability?
- A hypothesis
- A physical happening
- A possible outcome or combination of outcomes
- An experiment
An event in the context of probability refers to a possible outcome or combination of outcomes from a random experiment. For instance, if we toss a coin, the possible outcomes are 'Heads' and 'Tails'. Each of these outcomes is an event.
What's the probability of the union of two mutually exclusive events A and B?
- P(A) * P(B)
- P(A) + P(B)
- P(A) - P(B)
- P(A) / P(B)
The probability of the union of two mutually exclusive events A and B is given by P(A ∪ B) = P(A) + P(B). This is because mutually exclusive events cannot occur at the same time, so the probability of either event A occurring or event B occurring is the sum of their individual probabilities.
The alternative hypothesis, denoted by H1 or Ha, is the hypothesis that _______ observations are influenced by some non-random cause.
- Population
- Random
- Sample
- Systematic
The alternative hypothesis proposes that there is a difference or an effect in the population and the sample observations are influenced by some non-random cause.