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 ? = 8 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.)

  ,

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.)

(c) The statistical procedures used in (a) and (b) are valid when several assumptions are met. What are these assumptions? (Select all that apply.)

We must assume that the sample has an underlying distribution that is uniform.

We must assume that the 16 cuttings in our sample are an SRS.

Because our sample is not too large, the population should be normally distributed, or at least not extremely nonnormal.

Because our sample is not too large, the standard deviation of the population and sample must be less than 10.

Explanation / Answer

Ans:

a)

90% confidence interval for true mean

=145+/-1.645*(8/sqrt(16))

=145+/-3.29

=(141.71, 148.29)

b)

z=(145-140)/(8/sqrt(16))

z=2.5

p-value=P(z>2.5)=0.0062

c)

We must assume that the 16 cuttings in our sample are an SRS.

Because our sample is not too large, the population should be normally distributed, or at least not extremely nonnormal.

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