Answered: A personality questionnaire can be used…

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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A personality questionnaire can be used to measure the level of the respondent’s extroversion
on a scale between 1 and 50. In the general population, the mean score is 22.5, with a standard
deviation of 5.0. A random sample of 120 IT experts have filled in this questionnaire and the
mean extroversion score for this sample is 22.08. You wish to conduct a test of hypothesis at the
.10 level of significance to determine if the data provide evidence that IT experts are less
extroverted than average (i.e. the mean extraversion score for all IT experts in the population is
below 22.5). If the test statistic turns out to be less than a critical value, you will conclude that
you have evidence for your research hypothesis. What is the critical value? (Provide your answer
as a number rounded to 2 decimals.

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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