How strong a force (in pounds) is needed to pull apart pieces of wood 4 inches long and 1.5 inches square? The following are data from students performing a comparable laboratory exercise. Suppose that the strength of pieces of wood like these follow a Normal distribution with standard deviation 3000 pounds. 33,220 31,900 32,600 26,540 33,230 32,290 33,030 31,990 30,510 32,650 23,000 30,940 32,750 33,700 32,300 24,080 30,160 31,280 28,750 31,950 (a) We are interested in statistical significant evidence at the ? = 0.10 level for a claim that the mean is 32,500 pounds. What are the null and alternative hypotheses? H0: ? = 32,500 H1: ? < 32,500H0: ? = 32,500 H1: ? > 32,500 H0: ? = 32,500 H1: ? ≠ 32,500H0: ? ≠ 32,500 H1: ? = 32,500 What is the value of the test statistic. (Round your answer to two decimal places.) z = What is the P-value of the test? (Round your answer to four decimal places.) P-value = What is your conclusion? There is enough evidence to conclude that the wood's mean strength differs from 32,500 pounds.There is not enough evidence to conclude that the wood's mean strength differs from 32,500 pounds. (b) We are interested in statistical significant evidence at the ? = 0.10 level for a claim that the mean is 31,500 pounds. What are the null and alternative hypotheses? H0: ? = 31,500 H1: ? > 31,500H0: ? = 31,500 H1: ? ≠ 31,500 H0: ? = 31,500 H1: ? < 31,500H0: ? ≠ 31,500 Ha: ? = 31,500 What is the value of the test statistic. (Round your answer to two decimal places.) z = What is the P-value of the test? (Round your answer to four decimal places.) P-value = What is your conclusion? There is enough evidence to conclude that the wood's mean strength differs from 31,500 pounds.There is not enough evidence to conclude that the wood's mean strength differs from 31,500 pounds.

How strong a force (in pounds) is needed to pull apart pieces of wood 4 inches long and 1.5 inches square? The following are data from students performing a comparable laboratory exercise. Suppose that the strength of pieces of wood like these follow a Normal distribution with standard deviation 3000 pounds. 33,220 31,900 32,600 26,540 33,230 32,290 33,030 31,990 30,510 32,650 23,000 30,940 32,750 33,700 32,300 24,080 30,160 31,280 28,750 31,950 (a) We are interested in statistical significant evidence at the ? = 0.10 level for a claim that the mean is 32,500 pounds. What are the null and alternative hypotheses? H0: ? = 32,500 H1: ? < 32,500H0: ? = 32,500 H1: ? > 32,500 H0: ? = 32,500 H1: ? ≠ 32,500H0: ? ≠ 32,500 H1: ? = 32,500 What is the value of the test statistic. (Round your answer to two decimal places.) z = What is the P-value of the test? (Round your answer to four decimal places.) P-value = What is your conclusion? There is enough evidence to conclude that the wood's mean strength differs from 32,500 pounds.There is not enough evidence to conclude that the wood's mean strength differs from 32,500 pounds. (b) We are interested in statistical significant evidence at the ? = 0.10 level for a claim that the mean is 31,500 pounds. What are the null and alternative hypotheses? H0: ? = 31,500 H1: ? > 31,500H0: ? = 31,500 H1: ? ≠ 31,500 H0: ? = 31,500 H1: ? < 31,500H0: ? ≠ 31,500 Ha: ? = 31,500 What is the value of the test statistic. (Round your answer to two decimal places.) z = What is the P-value of the test? (Round your answer to four decimal places.) P-value = What is your conclusion? There is enough evidence to conclude that the wood's mean strength differs from 31,500 pounds.There is not enough evidence to conclude that the wood's mean strength differs from 31,500 pounds.

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

33,220	31,900	32,600	26,540	33,230
32,290	33,030	31,990	30,510	32,650
23,000	30,940	32,750	33,700	32,300
24,080	30,160	31,280	28,750	31,950

(a) We are interested in statistical significant evidence at the

? = 0.10

level for a claim that the mean is 32,500 pounds.

What are the null and alternative hypotheses?

H₀: ? = 32,500
H₁: ? < 32,500H₀: ? = 32,500
H₁: ? > 32,500 H₀: ? = 32,500
H₁: ? ≠ 32,500H₀: ? ≠ 32,500
H₁: ? = 32,500

What is the value of the test statistic. (Round your answer to two decimal places.)
z =

What is the P-value of the test? (Round your answer to four decimal places.)
P-value =

What is your conclusion?

There is enough evidence to conclude that the wood's mean strength differs from 32,500 pounds.There is not enough evidence to conclude that the wood's mean strength differs from 32,500 pounds.

(b) We are interested in statistical significant evidence at the

? = 0.10

level for a claim that the mean is 31,500 pounds.

What are the null and alternative hypotheses?

H₀: ? = 31,500
H₁: ? > 31,500H₀: ? = 31,500
H₁: ? ≠ 31,500 H₀: ? = 31,500
H₁: ? < 31,500H₀: ? ≠ 31,500
H_a: ? = 31,500

There is enough evidence to conclude that the wood's mean strength differs from 31,500 pounds.There is not enough evidence to conclude that the wood's mean strength differs from 31,500 pounds.

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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