An agronomist examines the cellulose content of a variety of alfalfa hay. Suppos

Question

An agronomist examines the cellulose content of a variety of alfalfa hay. Suppose that the cellulose content in the population has standard deviation = 9 milligrams per gram (mg/g). A sample of 16 cuttings has mean cellulose content x = 145 mg/g.

(a) Give a 90% confidence interval for the mean cellulose content in the population. (Round your answers to two decimal places.) (____,_____)

(b) 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. State H0 and Ha.

a. H0: = 140 mg/g; Ha: < 140 mg/g

b. H0: = 140 mg/g; Ha: 140 mg/g

c. H0: < 140 mg/g; Ha: = 140 mg/g

d. H0: > 140 mg/g; Ha: = 140 mg/g

e. H0: = 140 mg/g; Ha: > 140 mg/g

Carry out a significance test to see if the new data support this belief. (Use = 0.05. Round your value for z to two decimal places and round your P-value to four decimal places.)

z =

P-value =

Explanation / Answer

a)for above 90% CI, z=1.64485

hence confidence interval =mean +/- z*std error =141.299 ; 148.701

e. H0: = 140 mg/g; Ha: > 140 mg/g

2) std error =std deviation/(n)1/2 =2.25

hence test stat z=(145-140)/2.25 =2.222

p value =0.0131

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