A farmer is concerned that a change in fertilizer to an organic variant might change his crop yield. He subdivides 6 lots and uses the old fertilizer on one half of each lot and the new fertilizer on...

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A farmer is concerned that a change in fertilizer to an organic variant might change his crop yield. He subdivides 6 lots and uses the old fertilizer on one half of each lot and the new fertilizer on the other half. The following table shows the results.

a. Specify the competing hypotheses that determine whether there is any difference between the average crop yields from the use of the different fertilizers.


b. Assuming that crop yields are normally distributed, calculate the value of the test statistic.


c. At the 5% significance level, find the critical value(s).


d. Is there sufficient evident to conclude that the crop yields are different? Should the farmer be concerned?




Answered Same DayDec 25, 2021

Answer To: A farmer is concerned that a change in fertilizer to an organic variant might change his crop yield....

David answered on Dec 25 2021
131 Votes
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Suppose µd = true difference between older and newer fertilizer yields
Test: µd 6= 0 with t distn
Hypothesis test:
H0 : µd = 0 (Null Hypothesis)
Ha : µd 6= 0 (Alternative Hypothesis, also called H1)
This is two tailed test.
Differences (Older - Newer):
−2, 1, −3, 0, 1, −1
We calculate sample mean and std deviation from given data.
Sample Mean, d̄ =
∑
(d)
n
= −46 = −0.666667
Sample Variance, s2 =
∑
(d− d̄)2
n− 1 =
13.333333
5 = 2.666667
Sample std dev, s =
√
s2 =
√
2.666667 ≈ 1.632993
d =...
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