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  • Level: GCSE
  • Subject: Maths
  • Word count: 4209

GCSE Statistics Coursework

Extracts from this document...

Introduction

Kevin Sharp

Statistics GCSE coursework

Kevin Sharp

In my DT lesson our teacher told us to draw a 25cm line and I drew mine too big and the teacher told me to get better at maths. I did not think this would improve my ability to estimate a length of a line so decided to find out. The questions I thought up are:

1) Is there any relationship between estimating a length of a straight line linked to mathematical ability?

Null hypothesis: There is a relationship between them.

Alternative hypothesis: There is no relationship between them.

        2) Does the estimation of a non straight line improve after practice?

Null hypothesis: Practice improves the estimation of a non straight line.

Alternative hypothesis: Practice doesn’t improve the estimation of a non straight line.

        3) Does a 14/15 year olds ability to estimate the length of a straight line fit a normal distribution?

Null hypothesis: A 14/15 year olds ability to estimate a straight line fits normal distribution.

Alternative hypothesis: A 14/15 year olds ability to estimate a straight line doesn’t fit normal distribution.

4) Are a 14/15 year olds ability to estimate a straight line more accurate than estimating a non straight line?

Null hypothesis: A 14/15 year olds ability to estimate a straight line is more accurate than estimating a non straight line.

Alternative hypothesis: A 14/15 year olds ability to estimate a straight line is less accurate than estimating a non straight line.

To get this data I am going to test 14/15 year olds in England as they have the same amount of education and experience. 14/15 year old can be used as a sample of England’s population to some degree of accuracy.

...read more.

Middle

Y on X Regression Line: y=-0.4009x+67.42

Line of best fit: y=-0.4009x+67.42.

Both the line of best fit and the y on x regression line have the same equation.

The 67.42 shows where the line crosses the exam mark axis and the -0.4 gives the gradient of the line.

Substituting x = 43 in to the equation =-0.4009x+67.42, y = 50.1813  

So if a pupil estimated the line with a difference of 43 from the actual length, a rough estimate of what his exam result might be is 50%.

If you wanted to roughly estimate an estimate difference of a straight line from someone who got 59% in the year 9 end of year exam you could find out by using an x  dependant on y regression line.

This scatter graph shows the x  dependant on y regression line.

image05.png

x-on-y regression Line: x=-0.3949y+50.02

If someone got 59% in his exam then he may have estimated the straight line with a difference of about 27mm.

However these results are not very accurate as there is not a very strong correlation.

These results are related to my sample investigation. For the reasons stated at the beginning of my project I think that these results will relate both to the study population and the target population. However within these populations more variations of these results could be expected.

2) Does the estimation of a non straight line improve after practice?

Null hypothesis: Practice improves the estimation of a non straight line.

Alternative hypothesis: Practice doesn’t improve the estimation of a non straight line.

Sample:

I got 86 results for boys and 52 results for girls.

...read more.

Conclusion

Here is another histogram but showing the results between the 2nd +/- standard deviations:image11.png

Between the 2nd +/- standard deviations (-76 and 80) there is 93% of results. This is very close to 95% and shows a very strong similarity between the results and a normal distribution. As you can see, 100% of results are between the 3rd standard deviations and shows strong similarities between the results and a normal distribution.

My results are very close to a normal distribution showed by the amount of results between +/- 3 standard deviations and proves strongly my null hypothesis.

4) Are a 14/15 year olds ability to estimate a straight line more accurate than estimating a non straight line?

Null hypothesis: A 14/15 year olds ability to estimate a straight line is more accurate than estimating a non straight line.

Alternative hypothesis: A 14/15 year olds ability to estimate a straight line is less accurate than estimating a non straight line.

The sample used will be the same as used in question 2 and 3. The data I will use the distance from actual of a straight line and distance from actual of a non straight line before practise (before practise because the pupils did not have practise before estimating the straight line).

Here is the data I will use copied from excel:

St line length

Diff from 234

Non st.line length

Diff from 351

152

-82

185

-166

195

-39

238

-113

172

-62

172

-179

263

29

263

88

172

-62

172

179

189

-45

189

-162

320

86

290

-61

245

11

500

149

240

6

280

-71

250

16

340

-11

265

31

285

66

256

22

262

-89

210

-24

280

-71

258

24

308

43

210

-24

280

71

257

23

315

36

284

50

249

102

250

16

300

-51

200

-34

400

49

150

-84

480

129

250

16

180

171

226

-8

219

132

250

16

250

-101

270

36

270

81

200

-34

200

-151

250

16

250

-101

228

-6

314

37

181

-53

221

130

180

-54

245

-106

270

36

270

-81

232

-2

297

54

257

23

314

37

211

-23

300

51

200

-34

305

-46

230

-4

200

-151

274

40

424

-73

250

16

300

-51

240

6

310

41

200

-34

303

-48

255

21

355

-4

203

-31

450

-99

225

-9

225

-126

250

16

300

-51

282

48

357

6

186

-48

197

154

250

16

200

-151

240

6

210

-141

248

14

250

-101

175

-59

300

-51

240

6

310

-41

276

42

322

-29

270

36

350

-1

243

9

348

3

250

16

300

51

235

1

250

101

289

55

350

-1

182

-52

325

26

267

33

309

42

243

9

342

9

323

89

325

-26

241

7

363

-12

230

-4

410

59

245

11

315

36

232

-2

283

68

250

16

370

-19

137

-97

323

-28

176

-58

368

-17

240

6

230

-121

250

16

290

-61

250

16

370

19

274

40

349

2

209

-25

302

49

282

48

392

-41

285

51

428

-77

300

66

300

-51

210

-24

400

-49

300

66

400

-49

250

16

500

149

242

8

421

-70

270

36

411

-60

317

83

453

-102

268

34

244

107

272

38

433

-82

256

22

427

-76

200

-34

200

-151

217

-17

242

109

195

-39

152

-199

150

-84

200

-151

250

16

250

-101

200

-34

230

-121

...read more.

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