Answered: A carpenter is making doors that are…

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 carpenter is making doors that are 2058 millimeters tall. If the doors are too long they must be trimmed, and if they are too short they cannot be used. A sample of 61 doors is made, and it is found that they have a mean of 2044 millimeters with a variance of 729. Is there evidence at the 0.05 level that the doors are either too long or too short?

State the null and alternative hypotheses for the above scenario.

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: Given information

The provided information is as follows:
The population mean under the hypothesis is $straight mu equals 2058$ millimeters.
The total number of doors made is $straight n equals 61$ .
The sample mean is $straight x with bar on top equals 2044$ milimeters.
The sample variance is $straight s squared equals 729$ .
The level of significance is $straight alpha equals 0.05$