IB Math Applications and Interpretations - Tests of Significance

Ho = I will not crash out; Ha = I will crash out

One-Sample t-Test

Tests whether mean of a SINGLE SAMPLE is equal to given population mean

Two-Sample t-Test

Compares means of TWO INDEPENDENT groups to see if there’s a significant difference

Chi-Square Test of Goodness of Fit

Tests whether observed categorical data fits a theoretical/EXPECTED distribution

Chi-Square Test of Independence

Tests whether two categorical variables are INDEPENDENT or related

Null Hypothesis (H_O)

Default assumption → no significant difference/effect; usually involves EQUALITY or INDEPENDENCE

Alternative Hypothesis (H_A)

What you’re testing for → states there is a significant difference or that an effect exists; never includes equality (<, >, ≠)

If H_O is rejected, what does that make H_A?

True

Two-Tailed t-Test

Checking if two means are different in EITHER direction (≠) → use when question doesn’t specify direction of difference

One-Tailed t-Test

Checking if one mean is specifically GREATER/LESS THAN the other (>, <) → use when question specifies direction

If p > α…

The result is not statistically significant → fail to reject H_O (can’t support H_A

If p < α…

The result is statistically significant → reject H_O in favor of H_A (strong enough data to suggest a difference exists

What is the df of a One-Sample t-Test?

Sample size - 1

What is the df of a Two-Sample t-Test?

(Sample size 1 + Sample size 2) - 2

What is the df of a Chi-Square Test of Goodness of Fit?

Number of categories - 1

What is the df of a Chi-Square Test of Independence?

(Rows - 1)(Columns - 1)

What are H_O and H_A in a One-Sample t-Test?

H_O: μ = μ_o

H_A: μ ≠ μ_o

What are H_O and H_A in a Two-Sample t-Test?

H_O: μ₁ = μ₂

H_A: μ₁ ≠ μ₂

What are H_O and H_A in a Chi-Square Test of Goodness of Fit if expected values are the SAME?

H_O: μ₁ = μ₂ = μ₃

H_A: μ₁ ≠ μ₂ = μ₃

What are H_O and H_A in a Chi-Square Test of Goodness of Fit if expected values are DIFFERENT (x, y, z)?

H_O: μ₁ = x, μ₂ = y, μ₃ = z

H_A: μ₁ ≠ x, μ₂ = y, μ₃ = z

What are H_O and H_A in a Chi-Square Test of Independence?

H_O: The two variables are INDEPENDENT/have no association

H_A: The two variables are NOT independent/have an association