Chapter 6.5, Problem 1DC

Solution

To Calculate:

The mean of all the resampling differences between means collected by all pairs of students in Step 2 of Explore 1.

To State:

Is this mean close to the value of the most expected result when the null hypothesis is true.

The mean is $0.02$ and it is close to the value of the most expected result when the null hypothesis is true.

Given:

The values of $x_{\text{treatment}}-x_{\text{control}}$ :

Pair 1: $-0.28,-0.24,-0.18,-0.12,0.30$

Pair 2: $-0.26,0.00,0.12,0.18,0.28$

The null hypothesis is that “The soil nutrient has no effect on the yield of the cherry tomato plants.”.

Concepts Used:

Mean of $n$ observations is the sum of the observations divided by $n$ .

Calculations:

Determine the mean:

  $\begin{array}{c}\text{Mean}=\frac{1}{10}\left(-0.28-0.24-0.18-0.12+0.30-0.26+0.00+0.12+0.18+0.28\right)\\ =0.02\end{array}$

If the null hypothesis were true, then the difference between means should be zero. Note that the mean of all resampling differences is very close to zero. Hence, the mean is close to the value of the most expected result when the null hypothesis is true.

Conclusion:

The mean is $0.02$ and it is close to the value of the most expected result when the null hypothesis is true.