What does a larger sample size do to the sampling distribution of the mean?
- It decreases the spread of the distribution
- It does not affect the distribution
- It increases the spread of the distribution
- It skews the distribution
A larger sample size decreases the spread of the sampling distribution of the mean. This is because as the sample size increases, the standard error (a measure of the spread of the distribution of sample means) decreases, which means that the sampling distribution becomes more concentrated around the true population mean.
What is the relationship between the eigenvalue of a component and the variance of that component in PCA?
- It depends on the dataset
- There is no relationship
- They are directly proportional
- They are inversely proportional
The eigenvalue of a component in PCA is directly proportional to the variance of that component. In other words, a larger eigenvalue corresponds to a larger amount of variance explained by that principal component.
A Chi-square test for independence is used to determine if there is a significant relationship between two ________ variables.
- categorical
- continuous
- nominal
- ordinal
A Chi-square test for independence is used to determine if there is a significant relationship between two categorical variables. It is not applicable for continuous, ordinal, or nominal variables.
A probability must be a number between ________ and ________.
- #NAME?
- -1, 1
- 0, 1
- 1, 100
By definition, the probability of an event is a number between 0 and 1. A probability of 0 means the event will never occur, and a probability of 1 means the event is certain to occur.
What is the effect of having small expected frequencies in a Chi-square test?
- It does not affect the test
- It increases the power of the test
- It invalidates the test
- It reduces the power of the test
In a Chi-square test, having small expected frequencies can reduce the power of the test and potentially lead to erroneous conclusions. This is because the Chi-square test is based on the assumption that the expected frequency of each category is at least 5.
What is the role of standard error in interval estimation?
- Standard error determines the shape of the distribution of the sample means
- Standard error is not related to interval estimation
- Standard error is used to calculate the margin of error, which determines the width of the confidence interval
- Standard error is used to calculate the sample mean, which is the center of the confidence interval
The standard error plays a crucial role in interval estimation. It is used to calculate the margin of error, which determines the width of the confidence interval. The standard error measures the variability of the sample mean around the population mean. A smaller standard error will result in a narrower confidence interval, assuming the confidence level is constant.
Spearman's Rank Correlation is a ________ method that does not make assumptions about the distribution of data.
- Non-parametric
- Parametric
- Quantitative
- Univariate
Spearman's Rank Correlation is a non-parametric method, which means it does not make assumptions about the distribution of data. This makes it more flexible and robust than some parametric methods.
What conditions must be met for the Central Limit Theorem to hold true?
- The data must be collected without any bias.
- The data must be normally distributed.
- The sample must be a simple random sample, and the sample size must be sufficiently large (typically n > 30).
- The sample size must be less than 30.
The Central Limit Theorem generally applies when the following conditions are met: 1) The data should be sampled randomly, 2) The sample values must be independent of each other, and 3) The sample size should be sufficiently large (typically, n > 30 is considered sufficient).
In hypothesis testing, a Type II error is committed when the null hypothesis is ______ but we ______ to reject it.
- False, fail to reject
- False, reject
- True, fail to reject
- True, reject
A Type II error, also known as a false negative, occurs when we fail to reject a false null hypothesis. This means we've missed evidence of an effect or difference that truly exists.
What kind of relationship does Pearson's Correlation Coefficient measure?
- Exponential
- Linear
- Monotonic
- Non-linear
Pearson's correlation coefficient measures linear relationships between variables. It measures the degree to which pairs of data for these two variables lie on a line.