Aside

Launch a Project Experiment: Gibberellin and Brassinolide

AP Statistics Project Proposal

(It has to be an experiment, no observational study will be accepted)

Group members:

Name ID
Jiayi Liu 2014530054
Ziyi Wang 2014530070
Fan Xu 2014530268
Junhui He 2014530723
  1. Topic (What is the research question)

Comparison of the Effects of Gibberellin and Brassinolide on Soybean Seed Germination

  1. Sampling (Be specific about how subjects might be selected)

Randomly select 120 soybeans that are purchased from the same source.

  1. Variables:

Explanatory variables:

Type of plant hormone being used: categorical, no plant hormone (control), Gibberellin, Brassinolide, or both.

Response Variable: the height of seedlings after 2 days; the height of seedlings after 7 days.

  1. Treatment:

We have 4 kinds of treatments.

For the selected seeds, randomly assign them to different treatments, which is soaking the soybean seeds in specified solution for 12 hours. Each treatment has 30 seeds:

No plant hormone 10-6 mol/L Gibberellin
10-6 mol/L Brassinolide 5×10-7 mol/L Gibberellin + 5×10-7 mol/L Brassinolide

After soaking, transplant the seeds to soil. Water the seeds every 12 hours, take an account of the proportion of germinated seeds. Also measure the height of seedlings after 2 days and 7 days.

  1. What extraneous variables might influence the response?

Environmental factors, like temperature, light intensity, water, and even soil conditions all could have impact on seed germination.

  1. How does the design protect against its potential influence on the response through blocking, direct control, or randomization?

We would use preliminary experiment to ensure the optimal conditions for plant growth. Despite that, we would also apply:

Direct control: All the seeds are grown in the same room and are expose to the same environmental factors so that the extraneous factors’ effects are not confounded with those of the experimental variables.

Randomization: Randomly assign the seeds to different treatment groups to ensure that the experiment does not systematically favor one treatment over another.

Replication: There is considerable amount of individuals for each treatment to achieve an adequate number of observations for each experimental condition.

  1. Statistical method (e.g. we plan to use…method to explore … We hope to have a …result)

Normally, we would apply what we learned from descriptive statistics: Calculating important statistics, like the mean heights of seedlings, and representing them in the form of a bar chart for comparison.

For the part of inference, we plan to use two-sample t-test to explore whether there is a significant difference in the effects of different plant hormones in the heights of seedlings. We hope that there is significant difference so that we could have evidence to support that one plant hormone is greater in promoting germination than the other.

We also plan to use regression analysis to explore whether there is a linear relationship between the heights of seedlings after 2 days and those after 7 days for a specific treatment group, thus implicitly see if each hormone has prolonged effect.

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Conservation of Energy

  1. Target

To find the kinetic friction constant μ according to the conservation of energy principle.

  1. Theory

The conservation of energy experiment states that the total energy of an isolated system cannot change—it is said to be conserved over time. Energy can be neither created nor destroyed, but can change form.

Formula: Ek=Ug, W=Fd cos θ=ΔEk

  1. Experimental process

The known scalars are the mass of blocks M and m, and the M can be dragged to the left by the block m. However, the only tool we could use is ruler. So we need to calculate the relevant variables to get the expression of the μ.

pulley

Step 1: First of all, let the two blocks at rest.

Step 2: Release the m block, when the m block reaches the ground instantly, the first course ends and the M slides distance of h.

Step 3: Then the M still slides length of l to left and stops, this process is considered as the next course.

Step 4: During the two courses, using the law of conservation of energy or work-energy principle, we could get two equations to induce the μ.

  1. Data
M/kg m/kg h/m l/m Theoretical μ Average μ Error/%
1 0.198 0.2925 0.38 0.638 0.3165 0.2947 7.42%
2 0.198 0.2925 0.38 0.674 0.2946 0.2947 -0.01%
3 0.198 0.2925 0.38 0.670 0.2969 0.2947 0.77%
4 0.198 0.2925 0.38 0.673 0.2952 0.2947 0.19%
5 0.198 0.3225 0.38 0.642 0.2906 0.2947 -1.38%
6 0.198 0.3225 0.38 0.602 0.3160 0.2947 7.24%
7 0.198 0.3225 0.38 0.648 0.2871 0.2947 -2.56%
8 0.198 0.3225 0.38 0.646 0.2883 0.2947 -2.17%
9 0.198 0.3225 0.38 0.642 0.2906 0.2947 -1.38%
10 0.198 0.3925 0.38 0.564 0.2919 0.2947 -0.95%
11 0.198 0.3925 0.38 0.573 0.2860 0.2947 -2.95%
12 0.198 0.3925 0.38 0.572 0.2866 0.2947 -2.74%
13 0.198 0.3435 0.38 0.626 0.2853 0.2947 -3.18%
14 0.198 0.3435 0.38 0.606 0.2975 0.2947 0.96%
15 0.198 0.3435 0.38 0.607 0.2969 0.2947 0.75%

 

  1. Result

Assume that the ground UG=0, according to the law of energy conservation, during the first course, we could get:

mgh-μMgh=0.5Mv2

Therefore, μ=(mgh-0.5Mv2)/Mgh

During the second course, according to the work-energy principle, we could get:

μMgl=0.5Mv2

After that it is time for us to figure out the l.

Because μMgl=0.5Mv2,we just change the order of this formula, that is, l=(0.5Mv2)/μMg

 

  1. Error Analysis

During this experiment, there may be some errors occur inevitably. Here are some reasons.

First of all, it is not so appropriate for us to use ruler to measure the displacement driven by M, using ordinary timer can also cause some mistakes.

Secondly, to calculate the kinetic friction constant, we ignore the mass of the cord, and the friction between the cord and the pulley. This error is not so serious, but in a way, it should be put into one of the reasons.

To reduce the errors, I think the best way is to use some instruments that can measure the variables more accurately.