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Collect data with a view to estimating population parameters using estimation techniques.

Extracts from this document...

Introduction

Statistics Coursework

Task: You are required to collect data with a view to estimating population parameters using estimation techniques. This should involve taking a random sample as well as calculating and comparing confidence intervals.

I have decided to estimate the population parameters for sentence length in 2 different genres of books. I have chosen a horror book and a drama book to see how sentence length varies between them. In theory I would expect the horror book to have much shorter sentences to add suspense whilst I would expect the drama to have longer more descriptive sentences.

Method:

As it would be too time consuming to record the sentence length for the whole population (the whole book). I am going to use sampling. To try and avoid any bias I will use the random number function on a calculator to find a page in the book and then I will record the length of the first full sentence. I will take a 100 samples for each book as this is enough that I will be able to gain accurate estimates for the population parameters but not use too much time. If by chance 2 the random number function produces a number that has already been used I will simply take the length of the second sentence on that page.

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Middle

16

129

9

73

7

208

18

98

5

51

145

11

Data For Drama Book

Page

Sentence Length

51

19

148

20

234

29

114

18

195

6

313

4

239

19

115

11

10

2

203

9

191

8

118

21

109

10

317

4

217

9

298

9

241

9

10

6

232

10

57

11

114

32

80

11

196

14

49

11

67

9

282

15

280

31

226

18

71

24

315

16

308

5

203

9

226

14

147

38

224

10

236

19

185

18

257

5

317

11

1

29

169

15

66

9

267

17

106

20

232

28

160

37

300

25

322

8

49

21

26

29

276

41

214

15

233

7

131

9

76

8

71

8

317

9

177

5

155

13

266

6

95

5

308

3

93

6

55

8

96

4

311

6

65

9

128

21

288

18

203

4

210

19

166

20

175

14

280

13

249

8

245

19

182

4

312

19

52

23

73

13

221

6

204

12

73

13

189

9

129

25

50

25

230

6

273

22

218

12

31

39

149

28

96

7

48

14

80

18

13

11

167

4

34

23

43

10

94

7

49

16

The first thing for me to do is to find the Mean, Standard Deviation and Variance of the sample I have taken. As it would be extremely time consuming trying to find the exact mean and variance for 100 results I have set up frequency tables which will allow me

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Conclusion

Obviously this is highly impractical but it shows how inaccurate my estimate is due to the fact that I took so few samples. Also I only sampled 1 book from each genre so it is difficult for me to accurately say that all books from these genres will be the same. It is possible that different authors with different writing styles will produce different sentence lengths. For example another horror writer may use longer sentences whilst another drama writer might use shorter sentences.

So if I was to extend this investigation I would firstly take more samples to ensure greater accuracy which would therefore allow greater certainty in any conclusions drawn. Secondly I would compare a number of different horror books against each other to see if their population parameters were similar or if they varied. Another progression could be to sample a number of horror books by the same author to see if they are at all similar in their population parameters.

...read more.

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