What does a 95% confidence interval estimate?
- The mean of the sample
- The range within which 95% of the data points lie
- The standard deviation of the population
- The true population parameter with a 95% level of confidence
A 95% confidence interval estimates the range within which we are 95% confident that the true population parameter lies. It is not about the range of the data or the mean of the sample.
What are the limitations of using mean as a measure of central tendency?
- It can't be used with large data sets
- It can't be used with small data sets
- It is difficult to calculate
- It is highly sensitive to outliers
The main limitation of the mean as a measure of central tendency is that it is highly sensitive to outliers or extreme values. An outlier can skew the mean and make it a less accurate representation of the data. Moreover, mean does not describe the middle value or most common value in the dataset, which are often important characteristics.
What are the assumptions made by the Spearman’s Rank Correlation test?
- The data is continuous and the relationship is monotonic
- The data is normally distributed and linear
- The data is ordinal and the relationship is linear
- The data is ordinal or continuous and the relationship is monotonic
The Spearman’s Rank Correlation test assumes that the variables are ordinal or continuous and that the relationship between them is monotonic. It does not require the relationship to be linear or the data to be normally distributed.
_______ regression is a method used to handle multicollinearity by adding a degree of bias to the regression estimates.
- Logistic
- Polynomial
- Ridge
- Simple linear
Ridge regression handles multicollinearity by introducing a degree of bias to the regression estimates, reducing their variance, and making them more reliable.
What is the primary goal of random sampling?
- To always select the same individuals
- To ensure that every member of the population has an equal chance of being selected
- To select individuals who are likely to give the desired results
- To select the individuals who are easiest to reach
The primary goal of random sampling is to ensure that every member of the population has an equal chance of being selected. This helps to reduce bias and increase the likelihood that the sample is representative of the population, which makes the results more valid and generalizable.
The conditional probability of A given B is denoted as ________.
- P(A + B)
- P(A / B)
- P(A B)
- P(A ∩ B)
The conditional probability of A given B is denoted as P(A
What is the effect of monotonic transformations on Spearman’s rank correlation coefficient?
- They decrease the coefficient
- They don't affect the coefficient
- They increase the coefficient
- They make the coefficient negative
Monotonic transformations do not affect the Spearman’s rank correlation coefficient. This is because Spearman's correlation is based on the rank order of data, and monotonic transformations preserve this order.
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.
_______ 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.
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.
If A and B are independent events, the probability of both occurring is ________.
- P(A + B)
- P(A / B)
- P(A ∩ B)
- P(A ∪ B)
If A and B are independent events, the probability of both occurring is P(A ∩ B) which is equal to P(A) * P(B). This is the fundamental characteristic of independent events in probability.
How does sample size affect the width of a confidence interval?
- Increasing the sample size decreases the width of the confidence interval
- Increasing the sample size has no effect on the width of the confidence interval
- Increasing the sample size increases the width of the confidence interval
- The relationship between sample size and the width of the confidence interval is unpredictable
Increasing the sample size decreases the width of the confidence interval. The larger the sample size, the more information you have, and thus the less uncertainty (which translates into a smaller standard error and narrower confidence interval).