1.The distance in meters that a shoe can be used before first signs of wearing appears on it is taken from two samples of two top types of shoes from a brand. The chain wants to use this data to test the research (alternative) hypothesis that the mean distance for type 1 is lower than that of type 2.

Hint: (use excel to calculate mean and std.dev.)(12 marks)

Type 1 (in meters)

Type 2 (in meters)

450

269

367

312

181

267

299

245

185

239

111

189

192

288

283

307

225

346

317

261

212

199

a.What are the null and alternative hypothesis for this research?

b.What are the sample mean distance for type 1 and type 2? What are the sample standard deviation for the two types?

c.Compute the test statistic t used to test the hypothesis. Note that the population standard deviations are not known and therefore you cannot use the formula in Section 10.1 of your text book. Use the one in Section 10.2 instead.

d.Compute the degree of freedom for the test statistic t.

e.Can the chain conclude that the mean distance for type 1 is lower than that of type 2? Use the critical-value approach and = 0.05 to conduct the hypothesis test.

f.Construct a 95% confidence interval for the difference of mean distance for the two types.