Answered: 14. You would like to know how…

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

: (Null and Alternate Hypothesis, Rejection Region)

A. Ho: µ = 0; Ha: µ < 0; Rejection Region: z < -2.34

B. Ho: µD = 0; Ha: µD < 0; Rejection Region: t < -2.57

C. Ho: µ = 0; Ha: µ > 0; Rejection Region: z > 2.34

D. Ho: µD = 0; Ha: µD ≠ 0; Rejection Region: z < -2.58 or z > 2.58

E. Ho: µD = 0; Ha: µD ≠ 0; Rejection Region: t < -2.90 or t > 2.90

(Mean Difference, and Test Statistic)

A. µD = -1.889; t = -2.331

B. µD = -2.444; t = -9.891

C. µD = -1.889; z = -2.331

D. µD = -2.444; t = -2.331

E. µD = -211.278; z = 18.333

(p-value and conclusion)

A. p = 0.026; FRHo (No sufficient evidence to reject the claim)

B. p = 0.038; RHo (Sufficient evidence exists to reject the claim)

C. p = 0.038; FRHo (No sufficient evidence to reject the claim)

D. p = 0.016; RHo (Sufficient evidence exists to reject the claim)

E. p = 0.016; FRHo (No sufficient evidence to reject the claim)

14. You would like to know how effective a diet
program is at helping people lose weight. 18
over-weight people are randomly selected to
participate in the program. They are weighed
before and after the program and the results are
listed below. Do these results give evidence that
the diet program is effective at the 1%
significance level?
Participant 1
Before
After
2 3 4
5 6
227 211
185
220 190 158
175 215 195 155 230 207
Participant 7 8 9 10 11 12
Before
260 156 201
300 180
270
After
258 159 201 290 172 272
Before
After
Participant 13
13 14 15 16 17 18
293 183
205 151 291
166
290 185 200 146 287
166

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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