Question

The stem diameter of wheat is important because easy breakage of the wheat can interfere with harvesting the crop. The diameter of wheat is known to be normally distributed with a mean of 1.9 mm. An agronomist hypothesizes that the new fertilizer being used is increasing plant stem diameter. After 5 days from the flowering of the wheat, the agronomist measures the diameters (mm) of the plants. What can the agronomist conclude with an α of 0.01? The wheat diameters are as follows:
1.8, 2.6, 2.4, 1.7, 2.3, 2.5, 1.9, 2, 3, 1.2.

a) What is the appropriate test statistic?
---Select--- na z-test One-Sample t-test Independent-Samples t-test Related-Samples t-test

b)
Population:
---Select--- weeks stem diameter the new fertilizer sample of wheat grown average wheat
Sample:
---Select--- weeks stem diameter the new fertilizer sample of wheat grown average wheat

c) Compute the appropriate test statistic(s) to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
critical value =  ; test statistic =
Decision:  ---Select--- Reject H0 Fail to reject H0

d) If appropriate, compute the CI. If not appropriate, input "na" for both spaces below.
[  ,  ]

e) Compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
d =  ;   ---Select--- na trivial effect small effect medium effect large effect
r² =  ;   ---Select--- na trivial effect small effect medium effect large effect

f) Make an interpretation based on the results.

The wheat grown with the new fertilizer has a significantly larger diameter than average wheat.

The wheat grown with the new fertilizer has a significantly smaller diameter than average wheat.    

The wheat grown with the new fertilizer did not have a significantly different diameter than average wheat.

Answer 1

a) It is a one-sample t-test.

c)

The test statistic is =

where S = sample standard deviation.

here, , n=10

So t = 12.986, critical t = 2.821438

As p-value < 0.01, we reject the null hypothesis.

d) CI = [1.675057,)

e) na.

f) The wheat grown with the new fertilizer has a significantly larger diameter than average wheat.