An agronomist examines the cellulose content of a variety of alfalfa hay. Suppose that the cellulose content in the population is normally distributed. A sample of 15 cuttings has mean cellulose content of 145 milligram per gram of hay and a std dev of 8 milligram per gram of hay. A previous study claimed that the mean cellulose content was 140 mg/g, but the agronomist believes that the mean is higher than that figure. Test to see if the data support this belief at 1% level of significance. Write your answers to parts (a) through (e) below. (A ) Step-1: State the hypotheses ( H0 and H1 ), and identify the claim A. H0: μ = 140 H1: μ < 140 B. H0: μ = 145 H1: μ > 145 C. H0: μ > 140 H1: μ = 140 D. H0: μ = 140 H1: μ >140 ( b ) Step-2: Compute the P- value . Keep 4 decimals in your answer. A. 0.0392 B. 0.0783 C. 0.0148 D. 0.9652 ( c ) Step-3: Compare P- value with significance level value ( α value of 1% ) and make final conclusion about whether or not to reject the null hypothesis. A. Do not reject H0 since P-value is greater than alpha value B. Reject H0 since P-value is less than alpha value C. Rehect H0 since P-value is greater than alpha value ( d ) Step-4: Summarize the result ( your final conclusion ) in words. A. There is enough sample evidence to conclude that mean cellulose content of alfalfa hay is higher than 140 milligram per gram. B. There is NOT enough sample evidence to conclude that mean cellulose content of alfalfa hay is higher than 140 milligram per gram. ( e ) Explain the possible error made in the context of the problem. Is it Type I or Type II error? Type I Error: Concluding that the mean cellulose content of alfalfa hay is higher than 140 when in reality tmean cellulose content of alfalfa hay is 140. Type II Error: Concluding that the mean cellulose content of alfalfa hay is 140 milligram per gram. when in reality mean cellulose content of alfalfa hay is higher than 140.

An agronomist examines the cellulose content of a variety of alfalfa hay. Suppose that the cellulose content in the population is normally distributed. A sample of 15 cuttings has mean cellulose content of 145 milligram per gram of hay and a std dev of 8 milligram per gram of hay. A previous study claimed that the mean cellulose content was 140 mg/g, but the agronomist believes that the mean is higher than that figure. Test to see if the data support this belief at 1% level of significance. Write your answers to parts (a) through (e) below. (A ) Step-1: State the hypotheses ( H0 and H1 ), and identify the claim A. H0: μ = 140 H1: μ < 140 B. H0: μ = 145 H1: μ > 145 C. H0: μ > 140 H1: μ = 140 D. H0: μ = 140 H1: μ >140 ( b ) Step-2: Compute the P- value . Keep 4 decimals in your answer. A. 0.0392 B. 0.0783 C. 0.0148 D. 0.9652 ( c ) Step-3: Compare P- value with significance level value ( α value of 1% ) and make final conclusion about whether or not to reject the null hypothesis. A. Do not reject H0 since P-value is greater than alpha value B. Reject H0 since P-value is less than alpha value C. Rehect H0 since P-value is greater than alpha value ( d ) Step-4: Summarize the result ( your final conclusion ) in words. A. There is enough sample evidence to conclude that mean cellulose content of alfalfa hay is higher than 140 milligram per gram. B. There is NOT enough sample evidence to conclude that mean cellulose content of alfalfa hay is higher than 140 milligram per gram. ( e ) Explain the possible error made in the context of the problem. Is it Type I or Type II error? Type I Error: Concluding that the mean cellulose content of alfalfa hay is higher than 140 when in reality tmean cellulose content of alfalfa hay is 140. Type II Error: Concluding that the mean cellulose content of alfalfa hay is 140 milligram per gram. when in reality mean cellulose content of alfalfa hay is higher than 140.

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Description: An agronomist examines the cellulose content of a variety of alfalfa hay. Suppose that the cellulose content in the population is normally distributed. A sample of 15 cuttings has mean cellulose content of 145 milligram per gram of hay and a std dev

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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Test to see if the data support this belief at 1% level of significance.

Write your answers to parts (a) through (e) below.

(A ) Step-1: State the hypotheses ( H0 and H1 ), and identify the claim

A. H0: μ = 140 H1: μ < 140

B. H0: μ = 145 H1: μ > 145

C. H0: μ > 140 H1: μ = 140

D. H0: μ = 140 H1: μ >140

( b ) Step-2: Compute the P- value . Keep 4 decimals in your answer.

A. 0.0392

B. 0.0783

C. 0.0148

D. 0.9652

( c ) Step-3: Compare P- value with significance level value ( α value of 1% ) and make final conclusion about whether or not to reject the null hypothesis.

A. Do not reject H0 since P-value is greater than alpha value

B. Reject H0 since P-value is less than alpha value

C. Rehect H0 since P-value is greater than alpha value

( d ) Step-4: Summarize the result ( your final conclusion ) in words.

A. There is enough sample evidence to conclude that mean cellulose content of alfalfa hay is higher than 140 milligram per gram.

B. There is NOT enough sample evidence to conclude that mean cellulose content of alfalfa hay is higher than 140 milligram per gram.

( e ) Explain the possible error made in the context of the problem. Is it Type I or Type II error?

Type I Error: Concluding that the mean cellulose content of alfalfa hay is higher than 140 when in reality

tmean

cellulose content of alfalfa hay is 140.

Type II Error: Concluding that the mean cellulose content of alfalfa hay is 140 milligram per gram. when in reality mean cellulose content of alfalfa hay is higher than 140.

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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