The measure of how much individual sample means will vary is called the __________ error.
- Absolute
- Margin of
- Sampling
- Standard
The standard error of a statistic is a measure of the statistical accuracy of an estimate, equal to the standard deviation of the theoretical distribution of a large population of such estimates. It is used to test hypotheses on the grounds of a set of data. For sample means, the standard error tells us how the mean varies from one sample to another.
How does changing the units of measurement affect the standard deviation and variance of a dataset?
- It decreases them
- It depends on the new units
- It doesn't affect them
- It increases them
Changing the units of measurement will change the scale of the data, and hence will affect the values of standard deviation and variance. If the data is scaled up, both measures will increase, and if the data is scaled down, they will decrease. However, the relative dispersion, as measured by the coefficient of variation, will remain the same.
What is the principle of equally likely outcomes?
- All outcomes are equally probable
- All outcomes are identical
- All outcomes are independent
- All outcomes are mutually exclusive
The principle of equally likely outcomes is a basic assumption in the classical definition of probability. It states that if an experiment has n outcomes, and there's no reason to believe that any one outcome is more likely than any other, then each outcome is assumed to have an equal probability of 1/n. For example, in tossing a fair coin, heads and tails are equally likely.
If the p-value from a Mann-Whitney U test is less than the significance level, you would ________ the null hypothesis.
- accept
- either accept or reject
- fail to reject
- reject
If the p-value from a Mann-Whitney U test is less than the significance level (often 0.05), you would reject the null hypothesis, suggesting there is a significant difference between the groups.
What does the Law of Large Numbers state?
- It states that as the size of a sample is increased, the mean value of the sample will get closer to the mean or expected value of the population.
- It states that if an event is repeated under identical conditions, the probability of the event remains the same.
- It's a rule which states that the sum of the probabilities of all possible events is 1.
- It's the law that states the probability of an event is always constant.
The Law of Large Numbers states that as a sample size grows, its mean gets closer to the average of the whole population. In other words, as the number of experiments increases, the actual ratio of outcomes will converge on the theoretical, or expected, ratio of outcomes.
The graphical representation of residuals versus predicted values is known as a ________ plot.
- Box
- Histogram
- Residual
- Scatter
A Residual plot is a graph that shows the residuals on the vertical axis and the independent variable on the horizontal axis. If the points in a residual plot are randomly dispersed around the horizontal axis, a linear regression model is appropriate for the data; otherwise, a non-linear model is more appropriate.
What can the Mann-Whitney U test tell you about the shape of your distributions?
- It can confirm if your distributions are normal
- It can confirm if your distributions are skewed
- It can confirm if your distributions have equal variances
- It cannot tell you anything about the shape of your distributions
The Mann-Whitney U test does not provide information about the shape of the distributions. It is a non-parametric test that does not make any assumptions about the distribution of the data.
What is the purpose of multiple linear regression analysis?
- To classify data into different categories
- To cluster data into different groups
- To examine the relationship between several independent variables and a dependent variable
- To predict the outcome of a binary dependent variable
Multiple linear regression analysis is used to understand the relationship between several independent (explanatory) variables and a dependent (response) variable. It can also be used for predicting the mean value of the dependent variable given the values of the independent variables.
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.