ne students took the SAT test twice without doing any sort of preparatory course between the two tests. Their scores are listed below. Use the data to test the claim that in the population of all such​ students, the differences between the scores have mean 0.   Student A B C D E F G H I First score 480 510 530 540 550 560 600 620 660 Second score 460 500 530 520 580 590 560 640 690   a. Define the parameter     A. mu Subscript d Baseline equals   Mean of the first score   B. mu Subscript d Baseline equals   Mean of the second score   C. mu equals   Mean score   D. mu Subscript d Baseline equals   Mean of​ (First score​ - Second​ score)   b. State the null and alternative hypotheses     A. Upper H 0 : mu Subscript d Baseline equals 0 Upper H 1 : mu Subscript d Baseline greater than 0     B. Upper H 0 : mu Subscript d Baseline equals 0 Upper H 1 : mu Subscript d Baseline less than 0     C. Upper H 0 : mu Subscript d Baseline equals 0 Upper H 1 : mu Subscript d Baseline not equals 0     D. Upper H 0 : mu equals 0 Upper H 1 : mu not equals 0     c. Calculate the​ P-value. Which of these options is closest to its​ value?     A. 1.095     B. 0.903     C. 0.792     D. 0.807     d. State the technical conclusion     A. Do not reject Upper H 0     B. Reject Upper H 0     e. State the final conclusion     A. There is not sufficient sample evidence to support the claim.   B. There is not sufficient evidence to warrant rejection of the claim.   C. There is sufficient evidence to warrant rejection of the claim.   D. The sample data support the claim.   f. Does there appear to be any difference between the first and second​ scores?     A. No   B. Yes

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 + ...