Answered: Ten students were randomly selected…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 42PFA

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. Ten students were randomly selected from a high school to take part in a program designed to raise their reading
comprehension. Each student took a test before and after completing the program. The mean of the differences
between the score after the program and the score before the program is 16. It was decided that all students in the
school would take part in this program during the next school year. Let µA denote the mean score after the program
and µB denote the mean score before the program for all students in the school. The 95 percent confidence interval
estimate of the true mean difference for all students in the school is (9, 23). Which of the following statements is a
correct interpretation of this confidence interval?
(A) µA > µB with probability 0.95.
(B) µA < µB with probability 0.95.
(C) µA is around 23 and µB is around 9.
(D) For any µA and µB with ( µA - µB) ≥ 14, the sample result is quite likely.
(E) For any µA and µB with 9 < ( µA - µB) < 23, the sample result is quite likely.

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 + ...

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