In factor analysis, the relationship between each variable and the underlying factor is called a _______.
- factor correlation
- factor covariance
- factor loading
- factor variance
In factor analysis, the relationship between each variable and the underlying factor is called a factor loading.
What is a sample in the context of statistics?
- A chart showing population data
- A small group of people from a population
- A statistical calculation
- A type of population
In statistics, a sample refers to a subset of the population that is selected for study. The purpose of sampling is to draw conclusions about the entire population based on observations made on the sample. Since studying an entire population is often not feasible due to constraints such as time, cost, and accessibility, we rely on samples to gain insights about the population. Sampling, if done correctly, can provide a good approximation of the population and help in making inferences.
The process of estimation is made more precise by decreasing the _______ of the confidence interval.
- Confidence level
- Sample size
- Standard error
- Width
The precision of the estimation process increases as the width of the confidence interval decreases. A smaller width implies that the range of values within which the population parameter lies is narrower.
When is it appropriate to use quantitative data over qualitative data?
- Never
- When both measuring and categorizing are required
- When categorizing or describing is required
- When measuring or counting is required
Quantitative data is appropriate to use when measuring or counting is required, or when the data can be numerically quantified. This data type allows for statistical analysis and can provide a more objective and precise understanding than qualitative data. For example, it's appropriate to use quantitative data when you want to know how many people visited a website, how much customers are willing to pay for a product, or how often a certain event occurs.
What kind of hypothesis is tested in the Sign Test?
- The means of two groups are equal
- The medians of two groups are equal
- The proportions of two groups are equal
- The variances of two groups are equal
The Sign Test tests the null hypothesis that the medians of two groups are equal.
Bayes' theorem combines our prior knowledge about an event with evidence from data to provide a ________ probability.
- joint
- marginal
- posterior
- prior
The theorem combines our prior knowledge (the prior probability) and evidence (the likelihood) to provide a new, updated probability of an event (the posterior probability).
What are the components of a confidence interval?
- The population mean, the margin of error, and the level of confidence
- The population mean, the sample size, and the standard error
- The sample mean, the margin of error, and the level of confidence
- The sample mean, the population size, and the standard deviation
A confidence interval is composed of three parts: a point estimate (the sample mean), a margin of error (which depends on the standard error and the Z-value or T-value), and the level of confidence (which indicates the probability that the interval estimate contains the population parameter).
What does it mean when we say a non-parametric test makes fewer assumptions about the data distribution?
- The data distribution must be known
- The data does not have to follow a specific distribution, such as normal
- The data must be normally distributed
- The data must be uniformly distributed
When we say a non-parametric test makes fewer assumptions about the data distribution, we mean that the data does not have to follow a specific distribution, such as the normal distribution. Non-parametric tests are distribution-free tests and make no assumption about the probability distribution of the variables.
The Pearson's Correlation Coefficient measures the ________ between two variables.
- causal relationship
- linear correlation
- percentage similarity
- rank
Pearson's Correlation Coefficient measures the linear correlation between two variables. It quantifies the degree to which two variables are related to each other.
What is the null hypothesis in a one-way ANOVA test?
- All group means are different
- All group means are equal
- The sample is not representative of the population
- The variance is the same across all groups
The null hypothesis in a one-way ANOVA test is that all group means are equal. This hypothesis is tested against the alternative that at least one group mean is different.