Statistical Inference
What is the Central Limit Theorem?
The Central Limit Theorem states that, regardless of the shape of the population distribution, the sampling distribution of the sample means approaches a normal distribution as the sample size increases.
What is the definition of probability?
Probability is a measure of the likelihood or chance of an event occurring.
What is a random sample?
A random sample is a subset of individuals or items from a larger population, where each member has an equal chance of being selected.
What are the steps of hypothesis testing?
The steps of hypothesis testing are: (1) stating the null and alternative hypotheses, (2) selecting a significance level, (3) collecting and analyzing data, (4) calculating a test statistic, (5) determining the critical value or p-value, and (6) making a conclusion about the null hypothesis.
What is a null hypothesis?
The null hypothesis is a statement of no effect or no difference that is tested in statistical hypothesis testing.
What is the difference between independent and dependent events?
Independent events are not influenced by each other, while dependent events are influenced by each other's outcomes.
What is the difference between observational and experimental studies?
Observational studies observe individuals and variables without manipulating them, while experimental studies involve actively manipulating variables to observe their effects.
What is the difference between one-tailed and two-tailed tests?
In a one-tailed test, the alternative hypothesis is directional and focuses on one side of the distribution, while in a two-tailed test, the alternative hypothesis is non-directional and considers both sides of the distribution.
What is a p-value?
The p-value is the probability of obtaining a test statistic as extreme as, or more extreme than, the observed data, assuming the null hypothesis is true.
What is the difference between mutually exclusive and independent events?
Mutually exclusive events cannot occur at the same time, while independent events are not affected by each other's outcomes.
What is a confounding variable?
A confounding variable is an extraneous variable that is associated with both the independent and dependent variables, making it difficult to determine the true cause-and-effect relationship.
What is the critical value in hypothesis testing?
he critical value in hypothesis testing is the threshold value of a test statistic that separates the critical region (rejecting the null hypothesis) from the non-critical region (failing to reject the null hypothesis).
What is a Type I error?
A Type I error occurs when the null hypothesis is rejected, but it is actually true in the population.
What is conditional probability?
Conditional probability is the probability of an event occurring given that another event has already occurred.
What is a placebo effect?
The placebo effect refers to the phenomenon where a person's belief in receiving a treatment or intervention leads to a perceived improvement in their condition, even if the treatment itself has no active ingredients or effects.
What is the alternative hypothesis?
The alternative hypothesis is the hypothesis that contradicts the null hypothesis and is supported if there is sufficient evidence to reject the null hypothesis.
What is a confidence interval?
A confidence interval is a range of values constructed from sample data that is likely to contain the true population parameter with a certain level of confidence.
What is the law of large numbers?
The law of large numbers states that as the number of trials or observations increases, the observed outcomes will approach the expected probabilities or values.
What is sampling error?
Sampling error is the difference between a sample statistic and the corresponding population parameter, which occurs due to the inherent variability in samples.
What is the significance level?
The significance level, often denoted as alpha (α), is the predetermined threshold used to determine the level of evidence required to reject the null hypothesis. It represents the probability of rejecting the null hypothesis when it is true.