Answered: A corporation that maintains a large…

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 corporation that maintains a large fleet of company cars for the use of its sales staff is interested in the mean distance driven monthly per sales person. The following list gives the monthly distances in miles driven by a random sample of

10 sales persons.

2255 , 2610 , 2566 , 2645 , 2671, 1979, 2434, 2485, 2290, 2580

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Based on this sample, find a

95% confidence interval for the mean number of miles driven monthly by members of the sales staff, assuming that monthly driving distances are normally distributed. Then find the lower limit and upper limit of the

95% confidence interval.

Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.)

Lower limit:	?
Upper 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

$S a m p l e s i z e (n) = 10$

Here sample data is given hence we use T Test to find confidence interval

$\begin{array}{rcl} D e g r e e s o f f r e e d o m (d f) & = & n - 1 \\ = & 10 - 1 \\ = & 9 \end{array}$

$C o n f i d e n c e l e v e l = 0.95 (95 %)$

$\begin{array}{rcl} α & = & 1 - c o n f i d e n c e l e v e l \\ = & 1 - 0.95 \\ = & 0.05 \end{array}$

Using T table or Excel command =T.INV.2T(0.05,9) we find critical value

$C r i t i c a l v a l u e (t c) = 2.262$

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