A test of qualifying skills was taken by random samples of aspiring court reporters in both Iowa and Minnesota. Minnesotans had a mean score of 87.5, and Iowans had a mean score of 82.5 (out of 100). For each question below: In the first blank, type either "BT" for bootstrap, or "RND" for randomization. In the second blank, fill in the appropriate value, using your knowledge of these concepts. To estimate how much higher the Minnesota score is than the score for Iowa, the researcher constructs a confidence interval, using a  distribution,  which would be centered at the number, . To determine if the sample provides sufficient evidence that there is a difference between qualifying skills (as judged by mean scores on the test) of Minnesotans and Iowans, the researcher conducts a hypothesis test, making use of a  distribution, which would be centered at the number,

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...