Answered: A developmental psychologist would like…

Name: A developmental psychologist would like to determine how much fine mot
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Description: A developmental psychologist would like to determine how much fine motor skill changes for children from age 3 to age 4. He takes a random sample of 9 three-year old children and gives each a manual dexterity test that measures fine motor skill. He t

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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A developmental psychologist would like to determine how much fine motor skill changes for children from age 3 to age 4. He takes a random sample of 9 three-year old children and gives each a manual dexterity test that measures fine motor skill. He tests these same children a year later, when they are each four-years old. Higher scores on this test indicate better fine motor skills. Using the data in the table below, provide a point estimate, the 80% confidence interval, and the 90% confidence interval for the population mean of the difference scores.

Score at
Score at
3-years
33
46
4-years
36
48
27
35
44
50
36
45
30
39
39
35
40
46
35
42

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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