Answered: An educator want to determine whether…

Name: An educator want to determine whether early exposure to school affect
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Description: An educator want to determine whether early exposure to school affect IQ. He enlists the aid of parents of 24 of preschool age children to participate in this experiment, 12 children go to the preschool and 12 children stay at home. At the end of tw

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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An educator want to determine whether early exposure to school affect IQ. He enlists the aid of parents of 24 of preschool age children to participate in this experiment, 12 children go to the preschool and 12 children stay at home. At the end of two years, the IQs of all the children are measured. The results are as follows:

IQ of children who went to preschool.

110

121

107

117

115

112

130

116

111

120

117

106

IQ of children who stayed home.

114

118

103

112

117

106

125

113

109

122

116

104

what is the alternative and the null hypotheses?
what is the mean and standard deviation of each group?
what is the result and conclusion?

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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$N u l l H y p o t h e s i s (H_{0}) : μ_{x} = μ_{y}, t h e r e i s n o d i f f r e n c e b e t w e e n t h e m e a n I Q o f c h i l d r e n w h o w e r e p r e s c h o o l e d a n d w h o s t a y e d h o m e . A l t e r n a t e H y p o t h e s i s (H_{1}) : μ_{x} \neq μ_{y}, W h e r e μ_{x} a n d μ_{y} a r e t h e m e a n I Q o f t h e c h i d r e n w h o w e n t t o p r e s c h o o l a n d w h o s t a y e d h o m e r e s p e c t i v e l y$

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