You wish to test the following claim (Ha) at a significance level of α=0.005.       Ho:μ1=μ2       Ha:μ1>μ2 You obtain a sample of size n1=21 with a mean of M1=84.6 and a standard deviation of SD1=20.3 from the first population. You obtain a sample of size n2=27 with a mean of M2=82.1 and a standard deviation of SD2=11.5 from the second population.  Use the Theory-based inference applet to conduct the test of significance. (a)  What is the t-score for this sample?       t-score =   (Round to 2 decimal places.)  (b)  What is the p-value for this sample?       p-value =   (Round to 4 decimal places.) (c)  The p-value is... less than (or equal to) α

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 + ...