Question

1 exploration: resampling data
go to bigideasmath.com for an interactive tool to investigate this exploration.
work with a partner. a randomized comparative experiment tests whether water with dissolved calcium affects the yields of yellow squash plants. the table shows the results.
| yield (kilograms) |

control group	treatment group
1.0	1.1
1.2	1.3
1.5	1.4
0.9	1.2
1.1	1.0
1.4	1.7
0.8	1.8
0.9	1.1
1.3	1.1
1.6	1.8

a. find the mean yield of the control group and the mean yield of the treatment group. then find the difference of the two means. record the results.

b. write each yield measurement from the table on an equal - sized piece of paper. place the pieces of paper in a bag, shake, and randomly choose 10 pieces of paper. call this the “control” group, and call the 10 pieces in the bag the “treatment” group. then repeat part (a) and return the pieces to the bag. perform this resampling experiment five times.

c. how does the difference in the means of the control and treatment groups compare with the differences resulting from chance?

Explanation:

Step1: Calculate Control Group Mean

Sum of control group yields: \(1.0 + 1.2 + 1.5 + 0.9 + 1.1 + 1.4 + 0.8 + 0.9 + 1.3 + 1.6\)
\(= 10.7\)
Mean (control) = \(\frac{10.7}{10} = 1.07\)

Step2: Calculate Treatment Group Mean

Sum of treatment group yields: \(1.1 + 1.3 + 1.4 + 1.2 + 1.0 + 1.7 + 1.8 + 1.1 + 1.1 + 1.8\)
\(= 13.5\)
Mean (treatment) = \(\frac{13.5}{10} = 1.35\)

Step3: Find Difference of Means

Difference = \(1.07 - 1.35 = -0.28\) (or \(1.35 - 1.07 = 0.28\) in absolute)

Answer:

Control mean: \(1.07\) kg, Treatment mean: \(1.35\) kg, Difference: \(-0.28\) kg (or \(0.28\) kg absolute)