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I am new to this forum so here goes. I have an assignment question I need help with. A scientist has performed some experiments to determine the relationship between the concentration of phosphorus (P) in water and the concentration of the phosphorus in the water after 200 g of sand is added to the water. The idea is that some of the phosphorus will be absorbed into the sand, and we wish to know how much. As part of this experiment, the scientist added approximately 6000 units of phosphorus to a jug of water, mixed the phosphorus so that it was completely dissolved, and then poured all of this water into 3 smaller jugs so that there was an equal amount of water in each jug. This resulted in each jug containing approximately 2000 units of phosphorus. Initial measurements were then taken on the amount of phosphorus in each jug. Sand was then added to each jug, mixed, and the amount of phosphorus in the water in each jug was recorded again. Thus for each of the 3 jugs, there is an initial reading giving the amount of phosphorus in the water before adding the sand, and a final reading giving the amount of phosphorus in the water after adding the sand. I need to find a 95% CI for the amount of phosphorus absorbed into the sand. I haven't included figures from the example, but I don't know whether this is a paired t-test or not. I am thinking it is as each jug will be its own baseline, but I am only familiar with paired t-tests where we test if the difference is zero. Any help would be appreciated.

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    $\begingroup$ I've added the tag self-study as this is an assignment. Usually we expect you to have gone a bit further than this in sketching a solution. CV doesn't exist to do your assignments for you! $\endgroup$ – Nick Cox Aug 12 '13 at 14:23
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    $\begingroup$ Damien, please read the tag wiki info for the self-study tag. What have you tried? $\endgroup$ – Glen_b Aug 12 '13 at 14:27
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I think you've made some effort to solve this, so I'll give some hints.

"Paired" is a statistics term that means pretty close to its usual meaning. "Independent" means that one subject's data has no relation to another. So, are your data paired or independent?

As to this:

but I am only familiar with paired t-tests where we test if the difference is zero

Fine. Why is that not sufficient here?

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