Answered: Researchers asked two groups of people…

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

Researchers asked two groups of people to construct a jigsaw puzzle. One group of 55 people, who listened to soft classical music while working, had a mean construction time of 45 minutes. Another group of 45 people, who worked in silence, had a mean construction time of 55 minutes. Assume the population standard deviations for the construction times for people listening to classical music and people working in silence are 9.5 minutes and 11 minutes, respectively. Find the upper bound of the 99% confidence interval for the difference in population construction times between people listening to classical music as they work and people working in silence. Let the people listening to classical music be the first sample, and let the people working in silence be the second sample. Assume the samples are random and independent. Assume that both the population distributions are normally distributed. Round your answer to two decimal places. 90% confidence=1.645 95% confidence=1.96 99% confidence=2.576

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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