10.1 Confidence Intervals & the Difference of Means

two-sample t-interval for the difference between means

a confidence interval for the difference between the means of two independent groups - the number of degrees of freedom is given by a special formula

independent groups assumption

an assumption that states groups must be independent to compare their means - the assumption 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-methods

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

SE(ȳ₁ - ȳ₂) = √((s²₁/n₁) + (s²₂/n₂))

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

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 - the assumption can be checked using the randomization condition and the 10% condition

(ȳ₁ - ȳ₂) ± t*_df × SE(ȳ₁ - ȳ₂)

the formula used to calculate the confidence interval for the difference between the means of two independent groups

normal population assumption

an assumption that states that the populations the means represent must be considered normally distributed - the assumption 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 the sample size is 30 or greater, the shape of the distribution is unlikely to be a problem