Answered: The researchers conducted two…

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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The researchers conducted two single-sample t tests-one for each group comparing its mean to the expected mean (the population mean) of 13. Here are the results:

Hand-signature condition: (M=12.89,SD=3.98), t (27) = 0.14, p = 0.88

E-signature condition: (M=14.97,SD=5.05), t (30) = 2.17, p = 0.03

Based on the above results, did either condition differ significantly from the expected mean (the population mean) of 13?

a. Neither had a mean that was significantly different

b. Only the one's who signed by hand was significantly higher

c. Both were significantly higher on each side

d. Only the one's who signed electronically was significantly higher

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

The objective is to test the validity of the claims that, if the averages of the Hand-signature condition and the E-signature condition at the respective population levels are truly higher from the expected mean. For this, the p-values of the individual t-test are to be compared with the standard level of significance of 5% (i.e., $α = 0.05$ ).

The decision rule is: if $p - value \leq α$ , reject H₀ and if $p - value > α$ , H₀ is retained.