Quiz-2

What is a probability distribution?

• A probability distribution is a method for calculating averages.

• A probability distribution is a graphical representation of data.

• A probability distribution is a function that describes the likelihood of different outcomes for a random variable.

• A probability distribution is a type of statistical test.

Tags

NGSS.HS-LS4-3

Name two types of probability distributions.

• Geometric distribution

• Uniform distribution

• Exponential distribution

• Normal distribution, Binomial distribution

What is the purpose of hypothesis testing?

• The purpose of hypothesis testing is to determine if there is enough evidence in a sample to support a specific claim about a population.

• To eliminate all possible outcomes of an experiment.

• To collect data without any analysis.

• To prove a hypothesis is always true.

Tags

NGSS.HS-LS3-2

Define null hypothesis and alternative hypothesis.

• The null hypothesis suggests there is a significant effect, while the alternative hypothesis suggests no effect.

• The null hypothesis states there is no effect or difference, while the alternative hypothesis states there is an effect or difference.

• The null hypothesis states there is a difference, while the alternative hypothesis states there is no difference.

• The null hypothesis is always true, and the alternative hypothesis is never tested.

What does a p-value represent in hypothesis testing?

• A p-value represents the probability of obtaining results at least as extreme as the observed results, given that the null hypothesis is true.

• A p-value measures the effect size of the observed results.

• A p-value shows the likelihood of the alternative hypothesis being true.

• A p-value indicates the strength of the null hypothesis.

Explain the concept of a confidence interval.

• A confidence interval provides an estimated range of values which is likely to include an unknown population parameter, with a specified level of confidence.

• A confidence interval guarantees that the population parameter will fall within the calculated range.

• A confidence interval is a method to calculate the mean of a sample without any uncertainty.

• A confidence interval is a fixed value that represents the exact population parameter.

How is a confidence interval constructed?

• A confidence interval is constructed by taking the maximum and minimum values of the sample data.

• A confidence interval is constructed using the formula: population mean ± (z-score * sample size).

• A confidence interval is constructed using the formula: sample mean ± (critical value * standard error).

• A confidence interval is constructed using the formula: sample median ± (critical value * standard deviation).

What is the difference between a 95% and a 99% confidence interval?

• The 99% confidence interval is based on a different statistical method than the 95% interval.

• The difference is the sample size used for each interval.

• A 95% confidence interval is always wider than a 99% interval.

• The difference is the level of confidence: 95% is narrower and less confident than 99%, which is wider and more confident.

What is Bayesian inference?

• A way to visualize data using graphs and charts.

• Bayesian inference is a method of statistical inference that uses Bayes' theorem to update the probability of a hypothesis based on new evidence.

• A technique for random sampling from a population.

• A method for calculating the mean of a dataset.

How does Bayesian inference differ from frequentist statistics?

• Bayesian inference uses prior information and updates beliefs, whereas frequentist statistics focuses on the data from the current sample.

• Bayesian inference relies solely on the current sample data.

• Bayesian inference does not allow for updating beliefs over time.

• Frequentist statistics incorporates prior beliefs into its analysis.