A lumberyard has a machine that is designed to cut deck boards to a length of 14 feet. The manager of the lumberyard is concerned that the machine is not cutting the boards the correct length. He takes a random sample of 17 boards and records their lengths. Do these data provide convincing evidence at the = 0.05 level that the mean length of the cut boards differs from 14 feet? Let = the true mean length of the deck boards.Data: 13.89, 13.90, 13.95, 13.98, 13.99, 14.0, 14.02, 14.05, 14.08, 14.1, 14.15, 14.18, 14.2, 14.21, 14.23, 14.25, 14.3If needed, use the t-table to answer the question.What is the value of the test statistic? What is the P-value of the test? With a P-value = 0.05, we H0. There is evidence to conclude that the mean length of the cut boards is different from 14 feet. A lumberyard has a machine that is designed to cut deck If needed, use the t-table to answer the question.boards to a length of 14 feet. The manager of thelumberyard is concerned that the machine is not cuttingthe boards the correct length. He takes a random sampleof 17 boards and records their lengths. Do these dataprovide convincing evidence at the a = 0.05 level that themean length of the cut boards differs from 14 feet? Let u =the true mean length of the deck boards.What is the value of the test statistic?What is the P-value of the test?With a P-valuea = 0.05, weHo. There isv evidence toData: 13.89, 13.90, 13.95, 13.98, 13.99, 14.0, 14.02, conclude that the mean length of the cut boards is14.05, 14.08, 14.1, 14.15, 14.18, 14.2, 14.21, 14.23, different from 14 feet.14.25, 14.3

Given data is13.89, 13.90, 13.95, 13.98, 13.99, 14.0, 14.02, 14.05, 14.08, 14.1, 14.15, 14.18, 14.2, 14.21, 14.23, 14.25, 14.3sample size(n)=15α=0.05From given data Mean(x)=14.09standard deviation(s)=0.13The null and alternative hypothesis:-H0:μ=14Ha:μ≠14Test statistic(t):-t=x-μsnt=14.09-140.1315t=2.6813Test statistic(t)=2.6813P-value:-Degrees of freedom(df)=n-1=15-1=142P(t>|2.6813|)=0.0179 (from t-table)P-value = 0.0179with P-value is less than α=0.05 , we Reject H0.There is sufficient evidenceto conclude that the mean length of the cut boards is different from 14 feet

Answered: A lumberyard has a machine that is…

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 lumberyard has a machine that is designed to cut deck boards to a length of 14 feet. The manager of the lumberyard is concerned that the machine is not cutting the boards the correct length. He takes a random sample of 17 boards and records their lengths. Do these data provide convincing evidence at the = 0.05 level that the mean length of the cut boards differs from 14 feet? Let = the true mean length of the deck boards.

Data: 13.89, 13.90, 13.95, 13.98, 13.99, 14.0, 14.02, 14.05, 14.08, 14.1, 14.15, 14.18, 14.2, 14.21, 14.23, 14.25, 14.3

If needed, use the t-table to answer the question.

What is the value of the test statistic?

What is the P-value of the test?

With a P-value = 0.05, we H₀. There is evidence to conclude that the mean length of the cut boards is different from 14 feet.

A lumberyard has a machine that is designed to cut deck If needed, use the t-table to answer the question.
boards to a length of 14 feet. The manager of the
lumberyard is concerned that the machine is not cutting
the boards the correct length. He takes a random sample
of 17 boards and records their lengths. Do these data
provide convincing evidence at the a = 0.05 level that the
mean length of the cut boards differs from 14 feet? Let u =
the true mean length of the deck boards.
What is the value of the test statistic?
What is the P-value of the test?
With a P-value
a = 0.05, we
Ho. There is
v evidence to
Data: 13.89, 13.90, 13.95, 13.98, 13.99, 14.0, 14.02, conclude that the mean length of the cut boards is
14.05, 14.08, 14.1, 14.15, 14.18, 14.2, 14.21, 14.23, different from 14 feet.
14.25, 14.3

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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