10.2 Difference of Means Hypothesis Testing

t_df = (ȳ₁ - ȳ₂ - Δ₀) / (SE(ȳ₁ - ȳ₂))

the number of degrees of freedom for a two-sample t-test for the difference between means - use technology to determine this value

two-sample t-methods

a method that allows you to draw conclusions about the difference between the means of two independent groups - these have a special rule for estimating degrees of freedom

normal population assumption

an assumption that states the populations the means represent must be considered normally distributed - this can be checked using the nearly normal condition: if the sample size is less than 30, the data should be unimodal and symmetric, and if 30 or greater, the shape of the distribution is unlikely to be a problem

independence assumption

an assumption that states the data in each group must be drawn independently and at random or generated by a randomized comparative experiment - this can be checked using the randomization condition & the 10% condition

H₀ = μ₁ - μ₂ = Δ₀

the null hypothesis of the two-sample t-test for the difference between means - the hypothesized difference, Δ₀, is almost always zero

independent groups assumption

an assumption that states groups must be independent to compare their means - this can be checked by looking at how the data is gathered, and ensuring that there is no matching, pairing, or relations between each group of data

two-sample t-test for the difference between means

a hypothesis test for the difference between the means of two independent groups

SE((ȳ₁ - ȳ₂) = √((s₁²/n₁) + (s₂²/n₂))

the formula for calculating the standard error of the difference between two means