Answered: A random sample of 19 subjects was…

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

A random sample of 19 subjects was asked to perform a given task. The time in seconds it took each of them to complete the task is recorded below.

43, 28, 50, 34, 31, 43, 32, 48, 46, 28, 45, 35, 36, 32, 28, 42, 31, 42, 33

If we assume that the completion times are normally distributed, find a 90% confidence interval for the true mean completion time for this task. Give the lower limit and upper limit of the 90% confidence interval.

Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place.

Upper limit:

Lower limit:

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: we determine given and find mean and sd.

Let,

x: 43, 28, 50, 34, 31, 43, 32, 48, 46, 28, 45, 35, 36, 32, 28, 42, 31, 42, 33

$x with bar on top equals fraction numerator sum for i equals 1 of x over denominator n end fraction space stack x space with bar on top equals fraction numerator 43 plus space 28 plus space 50 plus space 34 plus space 31 plus space 43 plus space 32 plus space 48 plus space 46 plus space 28 plus space 45 plus space 35 plus space 36 plus space 32 plus space 28 plus space 42 plus 31 plus space 42 plus 33 over denominator 19 end fraction space x with bar on top space equals 707 over 19 x with bar on top space equals space 37.21$

$s equals square root of fraction numerator open parentheses x minus x with bar on top close parentheses squared over denominator n minus 1 end fraction end root s equals square root of fraction numerator 917.634 over denominator 19 minus 1 end fraction end root s equals 7.27$