Answered: Handy A factory hiring people to work…

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

Handy A factory hiring people to work on an assembly line
gives job applicants a test of manual agility. This test counts
how many strangely shaped pegs the applicant can fit into
matching holes in a one-minute period. The table below
summarizes the data by sex of the job applicant. Assume
that all conditions necessary for inference are met.

a) Find 95% confidence intervals for the average number
of pegs that males and females can each place.
b) Those intervals overlap. What does this suggest about
any sex-based difference in manual agility?
c) Find a 95% confidence interval for the difference in
the mean number of pegs that could be placed by men
and women.
d) What does this interval suggest about any difference in
manual agility between men and women?
e) The two results seem contradictory. Which method

is correct: doing two-sample inference or doing one-
sample inference twice?

f) Why don’t the results agree?

Male Female
Number of subjects 50 50
Pegs placed:
Mean 19.39 17.91
SD 2.52 3.39

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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