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Description: During a weight loss study, each of eight subjects were given a diet for 4 months. Use the table, which shows the weight for the ten subjects before and after having the diet for 4 months, to answer the following questions. Refer to chart below. What

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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During a weight loss study, each of eight subjects were given a diet for 4 months. Use the table, which shows the weight for the ten subjects before and after having the diet for 4 months, to answer the following questions. Refer to chart below.

What is the standard error of the mean difference?

What is the standardized test statistic t_s?

pound	1	2	3	4	5	6	7	8	Mean	SD
Weight after 4 months	168	177	196	180	229	144	197	252	192.88	34.34
Original weight	185	194	213	198	244	162	211	273	210	34.77
Difference	-17	-17	-17	-18	-15	-18	-14	-21	-17.13	2.10

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 + ...

Expert Solution

Step 1

Given,

Difference

-17

-18

-15

-18

-14

-21

-17.13

2.10

The mean of the difference is obtained as-

$\begin{array}{rcl} D & = & \frac{\sum_{i} d_{i}}{n} \\ = & \frac{- 17 + (- 17) + (- 17) + (- 18) + (- 15) + . . . . + (2.10)}{10} \\ = & \frac{- 152.03}{10} \\ = & - 15.203 \end{array}$

The standard deviation of the difference is obtained as-

$\begin{array}{rcl} S_{D} & = & \sqrt{\frac{\sum_{i} {(D - D)}^{2}}{n - 1}} \\ = & \sqrt{\frac{{[- 17 - (- 15.203)]}^{2} + {[- 17 - (- 15.203)]}^{2} + {[- 17 - (- 15.203)]}^{2} + . . . . + {[2.10 - (- 15.203)]}^{2}}{10 - 1}} \\ = & \sqrt{\frac{363.5348}{9}} \\ = & 6.35553 \end{array}$

The required standard error of the mean difference is obtained as-

$\begin{array}{rcl} S_{D} & = & \frac{S_{D}}{\sqrt{n}} \\ = & \frac{6.35553}{\sqrt{10}} \\ = & 2.00980 \end{array}$

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