Determine the decision criterion for rejecting the null the given hypothesis tes

Question

Determine the decision criterion for rejecting the null the given hypothesis test; i.e., describe the volutes of the test statistic that would result in rejection of the null hypothesis. A farmer has decided to use a new additive to grow his crops. He divided his farm into 10 plots and kept records of the corn yield (in bushels) before and after using the additive. The results are shown below. You wish to test the following hypothesis at the 5 percent level of significance. Obtain a 99% confidence interval about the difference of means mu_D. Interpret your CI. Use the CI for conducting the test of hypothesis as in part a.

Explanation / Answer

a.

Null Hypothesis : H0 : µd = 0

Alternative Hypothesis: Ha : µd 0

Here the test is matched paired data test for two direction.

First i will draw the difference table.

AVerage of the differences dbar = 0.9

Standard deviation of the difference sbar= 0.568

so Test statistic

t = (dbar )/ (sd / n) = 0.9 / (0.568/ 10) =  5.01

Here dF = 10 -1 = 9 and alpha = 0.05 and tcritical = 2.262

so here t < tcritical , so we can reject the null hypothesis and can conclude that there is significant difference in between corn yields after new additive than corn yields before new additive.

b. Here we have to calculate 99% confidence interval about the difference of means µd

Here 99 % CI = µd +- tcrit [sd / n) = 0.9 +- 3.250 *(0.568/ 10) = 0.9 +- 0.5838 = (1.484, 0.316)

So, the given confidence interval doesn't include value of Zero so we can reject the null hypothesis and can say that there is there is different yield by addition of additive then yield without addition of yield.

Plot Before After difference(d) 1 9 10 1 2 9 9 0 3 8 9 1 4 7 8 1 5 6 7 1 6 8 10 2 7 5 6 1 8 9 10 1 9 10 10 0 10 11 12 1 sum 9 Average 0.9 std. dev. 0.568

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