AP®︎ Statistics: Topic 4.3 Flashcards

“We are C% confident that the interval from a to b contains the true population mean or true population mean difference for the population of interest,” stated in context; for paired data, include the order of subtraction

In repeated random sampling from the same population with the same sample size, about C% of confidence intervals constructed by this method will contain the true population mean or true population mean difference

The population mean of one population of paired differences, defined using a specified order such as first measurement minus second measurement

The defined order used to compute each pair’s difference; it determines the meaning and sign of μd and must be stated in the interpretation

The values of μ or μd inside a confidence interval; they are reasonably consistent with the sample data at that confidence level

If k is outside a C% confidence interval, the interval provides evidence against μ = k or μd = k; if the whole interval is above k, there is evidence the parameter is greater than k, and if the whole interval is below k, there is evidence it is less than k

If k is in the interval, the data are consistent with μ = k or μd = k, so there is not convincing evidence at that level that the parameter differs from k

For matched pairs, 0 means no population mean difference; if 0 is outside the interval, there is evidence that μd is not 0, and if the whole interval is above or below 0, the sign shows the direction based on the defined order of subtraction

A value equal to a reported endpoint is treated as being in the interval, though rounding can make boundary conclusions uncertain

The half-width of a confidence interval; for a one-sample or matched-pairs t-interval, t*·s/√n

The full length of the confidence interval; for a one-sample or matched-pairs t-interval, 2t*·s/√n

t* increases, so margin of error increases and the interval gets wider; the midpoint stays the same

Holding confidence level and variability approximately constant, increasing n decreases the standard error, so the margin of error and interval width tend to decrease

For a fixed confidence level, interval width is approximately proportional to 1/√n

A two-sided C% confidence interval and a two-sided test at α = 1 - C/100 give corresponding conclusions: if k is outside the interval, reject H₀: μ = k; if k is in the interval, fail to reject, aside from rounding

A two-sided C% confidence interval and a two-sided test at α = 1 - C/100 give corresponding conclusions: if k is outside the interval, reject H₀: μ = k; if k is in the interval, fail to reject