Question

An agronomist examines the cellulose content of a variety of alfalfa hay. Suppose that the cellulose content in the population has standard deviation σ = 8 milligrams per gram (mg/g). A sample of 15 cuttings has mean cellulose content x = 144 mg/g.

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

z=

P-value=

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

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

b.We must assume that the 15 cuttings in our sample are an SRS

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

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

Answer 1

a ) To test :

Test statistic :

where ,

We reject H₀ if the

The value of the test statistic :

Now ,

Hence we reject the null hypothesis or H₀ .

Thus we have sufficient evidence to support the claim that the cellulose content is higher than 140 mg .

b )  b.We must assume that the 15 cuttings in our sample are an SRS

  d. Because our sample is not too large, the population should be normally distributed, or at least not extremely non-normal.