Be sure to identify any critical values you look up in a statistical table. As a
ID: 3021885 • Letter: B
Question
Be sure to identify any critical values you look up in a statistical table. As always, show all your work. I have a compost container which has been infested by these really interesting black soldier fly (BSF) larvae. I measured four of them and found lengths of 1.6, 1.0,1.4 and 2.0 cm. The variance of larval length is known to be 0.4. (Note that this is the variance of the length of a single larva, not the variance of the average of four lengths.) Your buddy says that the true mean length is 2.0 cm for BSF larvae. Test her hypothesis at the 10 percent level of significance and the 1 percent level of significance.Explanation / Answer
Formulating the null and alternative hypotheses,
Ho: u = 2
Ha: u =/ 2
As we can see, this is a two tailed test.
df = n - 1 = 3
Getting the test statistic, as
X = sample mean = 1.5
uo = hypothesized mean = 2
n = sample size = 4
s = standard deviation = sqrt(0.4) = 0.632455532
Thus, t = (X - uo) * sqrt(n) / s = -1.58113883
Also, the p value is
p = 0.211985443
As P > 0.1 and P > 0.01 we FAIL TO REJECT THE NULL HYPOTHESIS at 0.1 and 0.01 levels.
Hence, there is no significant evidence at 0.1 and 0.01 level that the true mean is not 2.0 cm. [CONCLUSION]