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...

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

<>

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.

Jun 04, 2022

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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...

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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...

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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...