Question

Below are 18 scores randomly selected from Professor Mahar's bowling scores. 148, 217, 182, 192, 192, 191, 204, 234, 179, 247, 199, 183, 171, 194, 214, 205, 215, 193 1. Construct a 95% confidence interval on the median of Professor Mahar's bowling scores Conduct a 95% confidence hypothesis test, using the Sign Test, to determine if Professor Mahar's median bowling score was greater than 190. Conduct a 95% confidence hypothesis test, using the Wilcoxon Signed Ranks Test, to determine if Professor Mahar's median bowling score was greater than 190. Which test would you be more likely to agree with? Why? a. b. c. d.

Answer 1

The confidence limits are given by actual values in the sample. We choose which values using the following formulae. n 1.96Vin 2 th ranked value 2 The upper 95% confidence limit is given by the: n 1.96Vn 2 7ranked value 2

148

171

179

182

183

191

192

192

193

194

199

204

205

214

215

217

234

247

Arranging the score in ascending order

n = 18

Lower limit = 18/2 -1.96*(18)^0.5 / 2

= 9 - 4.15 = 4.84 rank approx 5 that is =183

Upper limit = 1+9+4.15 =14.15 approx = 14th rank = 214

Approximate 95% confidence interval is given as [183,214]