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Name: In a study, 15 children were given blocks and told to build a tower as
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Description: In a study, 15 children were given blocks and told to build a tower as tall as possible. The time (in seconds) they took to finish the tower is recorded. After a month, the same 15 children repeated the same exercise. The difference in time (first ex

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 26PFA

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In a study, 15 children were given blocks and told to build a tower as tall as possible. The time (in seconds) they took to finish the tower is recorded. After a month, the same 15 children repeated the same exercise. The difference in time (first experiment minus second experiment) has a (sample) mean of 22.27 and a sample standard deviation of 32.77. Test the claim that there is a difference between the 2 times.

(a) What is the null hypothesis H0 and the alternative hypothesis H1?

(b) Using α=0.01, will you reject H0? Justify your answer by using a p-value.

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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