Lecture Notes on Hypothesis Testing

Flashcards covering key vocabulary and concepts from the lecture, focusing on hypothesis testing and statistical decision-making.

Alpha (α)

The probability that the null hypothesis (H0) is true, but the data leads to the conclusion that it is not. Represents the threshold for statistical significance.

Null Hypothesis (H0)

An initial belief or assumption about a population parameter (mean or proportion) that is tested against the sample data. Often states that the parameter is equal to a specific number.

μ (mu)

Represents the population mean, or the average value of a set of numbers for the entire population.

π (pi)

Represents the population proportion, or the percentage of successes (or failures) in a population.

x̄ (x-bar)

Represents the sample mean, which is an estimate of the population mean (μ) calculated from the sample data.

π̂ (pi-hat)

Represents the sample proportion, calculated as successes over trials. It's an estimate of the population proportion (π).

Hypothesis Test

A statistical procedure used to determine whether the data is close enough to our initial belief (null hypothesis) or if the initial belief is incorrect.

P-value

The probability of obtaining results as extreme as, or more extreme than, the observed results of a statistical hypothesis test, assuming that the null hypothesis is correct.

Test Statistic

A standardized value calculated from sample data during a hypothesis test. It's compared to a critical value to determine whether to reject the null hypothesis. (Calculated by StatCrunch)

Reject H0

The decision to reject the null hypothesis when the p-value is less than alpha, suggesting that the evidence contradicts the null hypothesis.

Fail to Reject H0

The decision to not reject the null hypothesis when the p-value is greater than or equal to alpha, suggesting that there is not enough evidence to contradict the null hypothesis.

Simple Random Sample

A subset of a statistical population in which each member of the subset has an equal probability of being chosen.

Assumptions

Conditions that must be met for a statistical test to be valid (ex. Normality) .

Concerns

Potential issues or biases in the data collection method (not a simple random sample) that could affect the results of the study.

Normality (Assumption)

Assuming data is normally distributed is needed in order to use T stat.

T-Test

A statistical test appropriate when sample size is less than 30 and we're not aware of the population standard deviation.

Z-Test

A statistical test appropriate when we're aware of population of the standard deviation and have a sample size of 30 data points or higher.