Explanation Given info: The data shows the 24 young adults at Washington University who listened to 100 pairs of speakers and were asked to indicate which of the two speakers was the taller within each pair. Calculation: PLAN : Check whether the mean number of correct identifications in the population of all young adults in the United States is greater than 50 or not. Let μ be the mean number of correct identifications in the population of all young adults in the United States. The null and alternative hypotheses are given below: Null hypothesis: H 0 : μ = 50 Alternative hypothesis: H a : μ > 50 SOLVE : Software procedure: Step-by-step procedure to obtain the test statistic, P -value and histogram using the MINITAB software is as follows: Choose Stat > Basic Statistics > 1-Sample t . In Samples in Column, enter the column of “ Tall ”. In Perform hypothesis test, enter the test mean as 50 . Check Options , enter Confidence level as 99.0 . Check graph , choose Histogram. Choose greater than in alternative

8th Edition

ISBN: 9781319042578

Author: David S. Moore, William I. Notz, Michael A. Fligner

Publisher: W. H. Freeman

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Question

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 + ...

Chapter 20.4, Problem 10AYK

To determine

To test: The claim that the mean number of correct identifications in the population of all young adults in the United States is greater than 50.

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Chapter 20 Solutions

The Basic Practice of Statistics

Ch. 20.1 - Prob. 1AYK Ch. 20.1 - Prob. 2AYK Ch. 20.2 - Prob. 3AYK Ch. 20.2 - Prob. 4AYK Ch. 20.3 - Prob. 5AYK Ch. 20.3 - Prob. 6AYK Ch. 20.3 - Prob. 7AYK Ch. 20.4 - Prob. 8AYK Ch. 20.4 - Prob. 9AYK Ch. 20.4 - Prob. 10AYK

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