Answered: Treatment Student 1 2 3 4 5 6 7 8 9 10…

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 group of college students volunteered to participate in a study investigating the effect of sleep deprivation on fine motor tasks. Each student was assigned to each of two treatments: staying awake all night and getting a full night’s sleep. The next morning at 8:00 a.m., the students are asked to thread as many needles as possible in five minutes. The treatments are administered on the first Saturday of consecutive months, and the order of the treatments is assigned to each student at random. The data table shows the number of needles successfully threaded by each student.

A 95% confidence interval for the mean difference in needles threaded is (1.33, 4.05). Based on this interval, should the researchers conclude that college students like the ones in this study thread the same number of needles when they are sleep deprived as when they are rested, on average?

A. Yes, the confidence interval contains only positive values.

B. Yes, one subject threaded more needles when sleep-deprived than when they were rested.

C. Yes, two subjects threaded the same number of needles when sleep-deprived as when they were rested.

D. No, the confidence interval does not contain 0, so there is evidence of a difference in needle-threading abilities.

E. No, almost all of the subjects threaded more needles when they were rested than when they were sleep deprived.

Treatment
1
Rested 9
6
Difference 3
Sleep Deprived
2 3 4 5
11 15 13 11
7
79
9
6 4
Student
6
7
10 8
968
4
A
2
0
8 9 10 11 12 13
16 13 10 9
77
1479
587
6
4 -1 0
2
1

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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