Question

Suppose that the cellulose content in the population has standard deviation o=9 milligrams per gram (mg/g). A sample of 16 cuttings has mean cellulose content x=144 mg/g. A previous study claimed that the mean cellulose content was u=140 mg/g, but the agronomist believes that the mean is higher than that figure. State Ho and Ha. Carry out a significance test to see if the new data supports this belief. (use a=0.05.

Answer 1

Solution:

Here, we have to use one sample z test for population mean.

Null hypothesis: H₀: The mean cellulose content is 140 mg/g.

Alternative hypothesis: H_a: The mean cellulose content is greater than 140 mg/g.

H₀: µ = 140 versus H_a: µ > 140

This is an upper tailed test.

We are given α = 0.05

Xbar = 144, n = 16, σ = 9

Test statistic formula is given as below:

Z = (Xbar - µ)/[σ/sqrt(n)]

Z = (144 – 140)/[9/sqrt(16)]

Z = 4/ 2.25

Z = 1.7778

P-value = 0.0377

(by using z-table)

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that the mean cellulose content is greater than 140 mg/g.

New data supports agronomist belief.