Answered: Do children diagnosed with attention…

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 7PPS

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Question

Do children diagnosed with attention deficit/hyperactivity disorder (ADHD) have smaller brains than children without this condition? Brain scans were completed for 152 children with ADHD and 139 children of similar age without ADHD. The mean brain size for the 152 children with ADHD was 1059.4 mL with a standard deviation of 117.5 mL. The mean brain size for the 139 children without ADHD was 1104.5 mL with a standard deviation of 111.3 mL.

How could you simulate one sample under the null hypothesis?

Take 152 red cards and 139 blue cards, shuffle the cards and randomly deal them into two piles of size 152 and 139. Calculate the difference in proportion of red cards between the two samples.

Write the children's brain sizes on 291 cards, shuffle the cards and randomly deal them into two piles of size 152 and 139. Calculate the difference in mean brain size between the two samples.

Write the children's brain sizes on 291 cards, shuffle the cards and randomly deal them into two piles of size 152 and 139. Calculate the difference in standard deviation of brain size between the two samples.

Write the children's ages on 291 cards, shuffle the cards and randomly deal them into two piles of size 152 and 139. Calculate the difference in mean age between the two samples.

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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