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Statistics coursework - hypotheses based on students statistics

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Introduction

Statistics coursework My hypotheses are as follows: ~ 1. Year 11 students are, on average, taller than year 9 students. 2. There is better correlation between height and weight in year 7 than there is in year 11. 3. The taller someone is the heavier they are. Below are the sampling methods that I have used in my coursework: Stratified Simple Random Stratified sampling can be defined as the process where the population is divided into a number of sub-groups, e.g. males aged 45-65. These subgroups are called strata, and the numbers sampled in the various strata are proportional to the size of the populations. E.g. if males aged 45-65 is known to compromise 13% of the total population in the UK, in a sample of 1000, 130 should be males aged 45-65. On the other hand, Simple Random sampling can be defined as the process by which every possible sample of a given size is equally likely to be selected. To ensure randomness and no bias, a random number table or RAN# on a calculator is used, and the items in the sampling frame are numbered. These two sampling methods were not used in isolation but combined to make full potential of both. For this investigation I will use a random stratified sample. This means that the data that I take the sample from is first sorted into strata and then a random sample is taken from them. The advantage for me using this type of sampling method was that the data was already in some sort of strata e.g. year groups, gender, weight, IQ, ideal for collecting the type of data I need in answering my hypotheses. The stratified sample method doesn't really have any sort of disadvantages. This is because using this type of sampling will use all of the data and none of the data will be biased unless its numerical or alphabetic order has any relevance or affect on the results. ...read more.

Middle

1.60 55 9 Ali Hannah 14 4 Female 102 1.62 52 9 Bennett Susan 14 3 Female 100 1.6 41 9 Brown Caroline 14 9 Female 108 1.59 48 9 Campbell Nichole 14 5 Female 116 1.57 62 9 Davies Davina 14 1 Female 107 1.55 52 9 Green Sahara 14 2 Female 100 1.54 54 9 Higgins Jade 14 4 Female 94 1.57 48 9 Jones Carly 14 8 Female 116 1.51 48 9 Langtle Rebekah 14 6 Female 100 1.51 65 9 McDonald Louise 14 1 Female 106 1.59 46 9 Packham Amanda 14 4 Female 106 1.65 49 9 Roberts Sarah 14 2 Female 93 1.54 45 9 Singh Karam 14 10 Female 106 1.49 40 9 Taylor Bethany 13 11 Female 1.52 48 9 Yates Christine 14 2 Female 108 1.64 42 10 Abejurouge Henry 15 3 Male 89 1.63 60 10 Bilton Jon 15 7 Male 88 1.55 64 10 Bushley George 15 1 Male 98 1.75 68 10 Dolt Anthony 15 8 Male 100 1.60 47 10 Hardy Jeff 15 0 Male 113 1.79 75 10 Jones Paul 15 5 Male 112 1.68 72 10 Larry Liam 15 5 Male 102 1.65 47 10 McManus Anthony 15 7 Male 90 1.73 50 10 Powers Anthony 15 9 Male 110 1.57 54 10 Singh Michael 15 7 Male 100 1.68 64 10 Spavin Peter 15 1 Male 88 1.63 50 10 Armstrong Sarah 15 2 Female 94 1.67 66 10 Brandward Amy 14 8 Female 76 1.65 53 10 Chayse Erica 15 10 Female 113 1.79 52 10 Fawn Attoosa 15 10 Female 119 1.73 45 10 Hall Faith 15 4 Female 110 1.55 48 10 Johnston Summer 14 11 Female 105 1.50 40 10 Martin Jane 15 4 Female 94 1.67 48 10 Peterson Tanya 15 7 Female 92 1.62 52 10 Simons Davina 15 1 Female 113 1.58 45 10 Spears Claire 15 6 Female 106 1.60 60 11 Askabat Fernado 16 2 Male 105 1.71 57 ...read more.

Conclusion

SCRC of year 7 = 6(432) = 0.77 15(152 - 1) SCRC of year 11 = 6(48) = 1.24 9(92 - 1) So from what I have said above about correlation and looking at my results I can now say that year 11 has a strong negative correlation and year 7 has a strong positive correlation. My third hypothesis was the heavier you are the more you weigh. And looking at my previous hypothesis I can predict that this will be true for my sample. This is because in my previous hypothesis the line of best fit was a strong positive correlation and also it had a positive gradient. This means that, as height increases so will your weight. But just to make sure that I am right I will carry out the procedure needed, which is to plot scatter graphs and then to analyse the results. From the above graphs it can clearly be seen that my hypothesis of as your height increases so will your weight. This is because from the graphs you can see that all the graphs have a positive gradient, which also means that there is a strong positive correlation. In conclusion I believe that my first, second and third hypothesis have beyond reasonable doubt been proven true, however to make sure that is what I want I will have to take a bigger sample. Also I will have to be able to use data from more than what looks like just one school. Also some of the data that I used did have some obvious errors in it and the anomalous results I got were excluded and another data sample was taken to replace the excluded ones. Some of the results may have been borderline so therefore they may have affected the results and made them unreliable. Overall I think that I got some reasonable and reliable results enough to prove my hypothesis. But for me to be totally sure that the results that I got from this were true and correct then I would have to take a bigger sample and then analyse it. ...read more.

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