Question

Suppose that Danielle, an avid gardener, would like to determine whether singing to her plants could help them grow taller.

She randomly assigned four jade plants to one of two groups, singing or no singing, and used the total height for each plant (in inches) after six weeks to determine plant growth.

Singing	33.2 (Plant 1)	33.6 (Plant 2)
No singing	33.0 (Plant 3)	33.3 (Plant 4)

There are six possible ways the four plants can be assigned to the two groups, with both groups having size ?=2.

Singing			No singing
Plant	Plant	Mean	Plant	Plant	Mean	Difference
Plant 1	Plant 2	33.4	Plant 3	Plant 4	33.15	0.25
Plant 1	Plant 3	33.1	Plant 2	Plant 4	33.45	−0.35
Plant 1	Plant 4	33.25	Plant 2	Plant 3	33.3	−0.05
Plant 2	Plant 3	33.3	Plant 1	Plant 4	33.25	0.05
Plant 2	Plant 4	33.45	Plant 1	Plant 3	33.1	0.35
Plant 3	Plant 4	33.15	Plant 1	Plant 2	33.4	−0.25

In ascending order, the mean differences are: −0.35, −0.25, −0.05, 0.05, 0.25, and 0.35.

With a null hypothesis of no difference, the two‑sided alternative hypothesis is that the mean plant height is different for the two groups, singing and no singing.

Carry out a permutation test of the hypotheses. Compute the ?-value. Round your answer to three decimal places.

?-value =

Answer 1