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.
What is the main difference between the Wilcoxon Signed Rank Test and the paired t-test?
- All of the above
- The Wilcoxon test is non-parametric while the t-test is parametric
- The Wilcoxon test is used for ordinal data while the t-test is used for continuous data
- The Wilcoxon test uses ranks while the t-test uses actual values
The Wilcoxon Signed Rank Test is a non-parametric test that uses ranks and is used for ordinal data, while the paired t-test is a parametric test that uses actual values and is typically used for continuous data.
The ________ in a two-way ANOVA can reveal whether the effect of one independent variable depends on the level of the other independent variable.
- Effect size
- Interaction effect
- Main effect
- Post-hoc test
The interaction effect in a two-way ANOVA reveals whether the effect of one independent variable depends on the level of the other independent variable. This allows us to understand how the independent variables relate to each other.
How is Bayes' theorem related to conditional probability?
- Bayes' theorem and conditional probability are not related
- Bayes' theorem cannot be used with conditional probability
- Bayes' theorem is a specific type of conditional probability
- Bayes' theorem is used to calculate the complement of the conditional probability
Bayes' theorem is a way of finding a probability when we know certain other probabilities. The probabilities that we know are usually conditional probabilities, and Bayes' theorem is used to 'reverse' these probabilities.
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.