The cuttlefish, a cephalopod and first cousin of the octopus, has the ability to camouflage to almost any natural sea environment instantaneously (within a few milliseconds). They are also able to camouflage to non-natural environments but not quite as quickly. A cognitive psychologist is interested in whether cuttles exhibit learning (by showing a reduction in reaction time) after repeated exposure to the same environment. Initially, 10 baby cuttlefish are individually placed in a tank with a checkerboard bottom and their reaction time (time to camouflage) is recorded. Over the next month the samecuttlefish are exposed to the same environment daily and at the end of the month each cuttlefish's reaction time is recorded again. The data are recorded in the table below. Reaction Time (seconds) Subject Before After 1 58 41 2 48 45 3 54 40 4 56 42 5 55 48 6 55 41 7 43 32 8 51 44 9 62 38 10 35 36 Use an alpha of 0.05 to determine if the repeated exposure to the checkerboard indeed changed reaction time. What type of error is possible based on the outcome? On average, do the cuttlefish take longer to react before or after the training? Report the means for both testing times.

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Description: The cuttlefish, a cephalopod and first cousin of the octopus, has the ability to camouflage to almost any natural sea environment instantaneously (within a few milliseconds). They are also able to camouflage to non-natural environments but not quite

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

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The cuttlefish, a cephalopod and first cousin of the octopus, has the ability to camouflage to almost any natural sea environment instantaneously (within a few milliseconds). They are also able to camouflage to non-natural environments but not quite as quickly. A cognitive psychologist is interested in whether cuttles exhibit learning (by showing a reduction in reaction time) after repeated exposure to the same environment. Initially, 10 baby cuttlefish are individually placed in a tank with a checkerboard bottom and their reaction time (time to camouflage) is recorded. Over the next month the samecuttlefish are exposed to the same environment daily and at the end of the month each cuttlefish's reaction time is recorded again. The data are recorded in the table below.

	Reaction Time (seconds)
Subject	Before	After
1	58	41
2	48	45
3	54	40
4	56	42
5	55	48
6	55	41
7	43	32
8	51	44
9	62	38
10	35	36

Use an alpha of 0.05 to determine if the repeated exposure to the checkerboard indeed changed reaction time.

What type of error is possible based on the outcome?

On average, do the cuttlefish take longer to react before or after the training? Report the means for both testing times.

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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