Answered: A neuroscientist is interested in…

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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Question

A neuroscientist is interested in testing the effects of environment on dendritic branching in the hippocampus (dendrites increase the receptivity of neurons and may be an important basis of cognition). To test this, he took one group of rats (n = 11) and housed them in an “enriched” environment (consisting of a large box with tunnels to run through, toys to play with, etc.) and then he took another group of rats (n = 11) and housed them in an “isolate” environment (rats were housed alone without any tunnels or toys). After 6 weeks, the number of dendritic spines in a particular region of the hippocampus from these rats was imaged and counted. The results are below. Did the different housing conditions have an effect on the number of dendrite branches? Solve using the steps in hypothesis testing.

Enriched condition

Isolate condition

Mean number of dendrites

(Estimated) Standard

Deviation

Question: Calculate the lower 95% confidence interval of the difference

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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