Key Concepts in Hypothesis Testing and Regression Analysis

p-value smaller than alpha

Reject the null hypothesis.

null hypothesis for claim 'greater than 24'

Null hypothesis: ≤ 24 (we test the opposite of the claim).

test statistic

Whether a null hypothesis should be rejected.

random sample in a finite population

Choosing randomly and taking the smallest number possible.

distribution when sigma is known

Normal distribution.

distribution when sigma is unknown

T-distribution.

central limit theorem usage

When the sample size is large, the distribution of the sample mean becomes approximately normal.

smaller p-value indication

More evidence against the null hypothesis.

confidence coefficient

1 - α (alpha).

coefficient of determination (r²)

The proportion of variation in the dependent variable explained by the independent variable.

independent variable in scatter diagram

The horizontal axis.

Least Squares Method

Minimizes the sum of the squared deviations (errors).

positive slope in simple linear regression

A positive relationship between the independent and dependent variables.

matched sample

Each data value in one sample is paired with a corresponding data value in another.

reason for using matched samples

They have less variance and are used when comparing related or paired variables.

error as sample size increases

The error decreases.

sample size and variance in matched samples

Smaller sample size generally means less variance in matched samples.

sampling distribution

The probability distribution of all possible values of the sample mean (x̄).

test comparing means of two samples

T-test.

Sample Coefficient Multiply

Multiplies sample data to calculate estimates (e.g., in regression).