If a distribution is flatter than a normal distribution, it is said to have negative ________.
- Kurtosis
- Mean
- Skewness
- Variance
If a distribution is flatter than a normal distribution, it is said to have negative kurtosis. This type of distribution has lighter tails and a flatter peak than the normal distribution. It is also called platykurtic.
How does the choice of significance level (α) affect the conclusion of a Chi-square test for goodness of fit?
- A higher α makes it easier to reject the null hypothesis
- A higher α makes it harder to reject the null hypothesis
- α has no impact on the conclusion of the test
- α only affects the power of the test, not the conclusion
A higher significance level (α) increases the likelihood of rejecting the null hypothesis. This is because you're setting a higher bar for the amount of evidence needed to retain the null hypothesis.
How does the sample size affect the standard error of a sample mean?
- Larger sample sizes decrease the standard error
- Larger sample sizes increase the standard error
- Smaller sample sizes decrease the standard error
- The sample size has no effect on the standard error
The sample size has an inverse relationship with the standard error of a sample mean. As the sample size increases, the standard error decreases. This is because larger samples provide a better approximation of the population, reducing the variability of the sample mean around the population mean.
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.