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# Bivariate Data - The aim of this coursework is to discover whether there is a correlation between the heights of people and there shoe size.

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Introduction

Unit 2614: Statistics 2:

Bivariate Data

Aim

The aim of this coursework is to discover whether there is a correlation between the heights of people and there shoe size. Is it true that if you are taller, your shoe size is bigger? In this investigation, I deem to find that out. This information would then be used to inform specialist clothes shows that tailor for tall men, which shoe sizes to stock. Should a shop that sells clothes for men over 6ft stock shoes which range from size 6 up to size 15? Or would it be more appropriate for them to just stock from sizes 10 -15?

Data collection

The population is adults who shop in Shirley, Birmingham. When I was working in a supermarket, I asked the first 50 people from 6pm onwards if they would fill in my table. The sampling method I have used is definitely not random however; it is suitable for this investigation. The conclusion

Middle

93.6192

-22.38

-2.84

500.8644

8.0656

63.5592

-21.38

-2.84

457.1044

8.0656

60.7192

-19.38

-1.84

375.5844

3.3856

35.6592

-18.38

-1.84

337.8244

3.3856

33.8192

-17.38

-1.84

302.0644

3.3856

31.9792

-16.38

-2.84

268.3044

8.0656

46.5192

-15.38

-2.84

236.5444

8.0656

43.6792

-13.38

-0.84

179.0244

0.7056

11.2392

-11.38

-0.84

129.5044

0.7056

9.5592

-11.38

-1.84

129.5044

3.3856

20.9392

-9.38

-0.84

87.9844

0.7056

7.8792

-8.38

0.16

70.2244

0.0256

-1.3408

-8.38

-0.84

70.2244

0.7056

7.0392

-7.38

-0.84

54.4644

0.7056

6.1992

-7.38

-0.84

54.4644

0.7056

6.1992

-6.38

0.16

40.7044

0.0256

-1.0208

-5.38

0.16

28.9444

0.0256

-0.8608

-4.38

-0.84

19.1844

0.7056

3.6792

-3.38

0.16

11.4244

0.0256

-0.5408

Conclusion

I am going to use the ‘standard’ 5% significance level to carry out my hypothesis test. The critical value for n = 50 at the 5% significance level for a 1-tail test is found from the product moment correlation coefficient tables to be 0.2353.

Since 0.8948 > 0.2353, the critical value, the null hypothesis is accepted.

The evidence from this small sample suggests that if you are taller, your shoe size is bigger however it is important not to rely on this data too much. This conclusion is only fairly accurate for adults. It is important to bear in mind that the conclusion could well be different for growing teenagers or younger children. The sampling technique could be improved by covering different ages of people. To get a more realistic perception of whether height affects shoe size then the sampling technique has to be much more random. An example of a more randomised test could be a proportional stratified sample, including the elderly, young, and middle aged people. Stratified sampling will usually lead to more accurate results about the entire population, and will also give useful information about the individual strata.

This student written piece of work is one of many that can be found in our AS and A Level Probability & Statistics section.

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