# Statistical Experiment Plan to investigate the ability to estimate 30 and 60 seconds.

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Introduction

I am interested in investigating the ability of teenager at estimating periods of time, and also seeing how the data of people estimating periods of time is spread out. I am doing this because I want to see if there is relationship between the estimate of periods of time. So if someone is good at estimating one period of time they are also good at estimating another similar period of time. Also I want to see how the data of people estimating time periods is spread out.

My hypotheses are:

Year 11 are better at estimating 60 seconds than year 7 s

The better you are at estimating 30 seconds the better you are at estimating 60 seconds

Year 11 data follows the normal distribution.

I want to investigate hypothesis one because I want to see if age has an effect on the ability to estimate. I believe this as elder students have had a longer education and due to this they generally have a better grasp at estimating time than year 7's who would, I believe would underestimate because they are younger and do not have a good grasp of estimating a second and have little or no relationships between their pieces of data as they fundamentally don’t understand how to estimate periods of time.

Year 11 are better at estimating 30 and 60 seconds than year 7 s

For hypothesis 1 I will collect all my data from Winston Churchill School as I can easily and quickly obtain data from the school. I will collect as much data as I can from year 11's and year 7's estimating 60 and 30 seconds and this will be my population. From my population I will take 2 separate stratified samples one for each year.

Middle

From these two samples I will draw 2 box plots. Box plots are good because they allow me to compare the consistency of a group of data (IQR), the average of a group of data (median), and the spread of a group of data (skew).

I want each box plots to be on the same scale so I am able to directing compare the two box plots. Also I want one year group to have a considerably higher median than the other year at least greater than 5 seconds furthermore it should be more consistent, so has a smaller IQR. Upon looking at the box plots I will see if there is a difference and if one year group is clearly better than the other. and if I will reject my hypothesis or nor. If I accept hypothesis 1 then I will investigate my second hypothesis and third hypothesis- The better you are at estimating 30 seconds the better you are at estimating 60 seconds Using year 11’s due to them being better at estimating periods of time so they will have a better correlation in the two estimates I believe. If my box plots show that year 7’s are better at estimating 30/60 seconds then I shall use year 7's for hypothesis 2 and 3.

HYPOTHESIS 2

The better you are at estimating 30 seconds the better you are at estimating 60 seconds

I am interested in investigating this hypothesis because I believe that people who estimate two periods of time different from each other i.e. 30 and 60 seconds will have correlation so if one is bad at estimating 30 seconds then they there estimate for 60 seconds will also be bad.

Conclusion

My acceptance criteria to accept this hypothesis is that for the percentage within 1 SD it has to be between 65%-71% as this value is close to 68%. For the percentage in 2 SD I will allow it to be between 93%-96% and for 3SD I will allow between 99% -100%. The reason I chose these percentages is because the normal distribution doesn’t exist exactly in reality but is similar and because I used a sample not my whole population so I have less data to work the percentages with so might be a few percent off.

H1 Year 11 are better at estimating 60 seconds than year 7 s H2 The better you are at estimating 30 seconds the better you are at estimating 60 seconds H3 Year 11 data follows the normal distribution.

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