# Statistic

**Topics:**Statistics, Confidence interval, Statistical hypothesis testing

**Pages:**7 (583 words)

**Published:**April 4, 2013

This report is about the case study of PAR, INC. From the following book: Statistics for Business an Economics, 8th edition by D.R. Anderson, D.J. Sweeney and Th.A. Williams, publisher: Dave Shaut. The case is described at page 416, chapter 10.

2. Problem statement

Par, Inc. has produced a new type of golf ball. The company wants to know if this new type of golf ball is comparable to the old ones. Therefore they did a test, which consists out of 40 trials with the current and 40 trials with the new golf balls. The testing was performed with a mechanical fitting machine so that any difference between the mean distances for the two models could be attributed to a difference in the design. The outcomes are given in the table of appendix 1.

3. Hypothesis testing

The first thing to do is to formulate and present the rationale for a hypothesis test that Par, Inc. could use to compare the driving distance of the current and new golf balls. By formulation of these hypothesis there is assumed that the new and current golf balls show no significant difference to each other. The hypothesis and alternative hypothesis are formulated as follow:

Question 1

H0 : µ1 - µ2 = 0 (they are the same)

Ha : µ1 - µ2 ≠ 0 (the are not the same)

4. P-value

Secondly; analyze the data to provide the hypothesis testing conclusion. The p-value for the test is:

Question 2

Note: the statistical data is provide in § 5.

-one machine

-two populations

-no other influences mentioned

-independently chosen

Conclusion: Independent sample

Table Standard Normal Distribution (inside the cover of the book)

z = 1.33 p = 2x (0.5- 0.4082) = 0.1836

This is a likely value so: not reject H0.

Recommendation: Take the new balls in production.

5. Statistical summary

Question 3:

Thirdly a descriptive statistical summery of the data is provide in the table below.

Current (1)

Mean270,275

Standard Error1,383968421

Median270

Mode272

Standard Deviation8,752984839

Sample Variance76,61474359

Range34

Minimum255

Maximum289

Sum10811

Count40

New (2)

Mean267,5

Standard Error1,564837994

Median265

Mode263

Standard Deviation9,896904463

Sample Variance97,94871795

Range39

Minimum250

Maximum289

Sum10700

Count40

This general data is used to calculate the other statistical test.

6. 95% Confidence interval

Question 4

Determine the 95% confidence interval for the population mean of each model.

Current golf balls

To calculate this, the general formula is used which says:

By filling in this formula the following equation is founded and solved to calculate the answer:

New golf balls

To calculate this, the general formula is used which says:

By filling in this formula the following equation is founded and solved to calculate the answer:

Difference between the means of the population

To calculate this, the general formula is used which says:

By filling in this formula the following equation is founded and solved to calculate the answer:

Question 5

By taking a larger sample size the standard deviation would decrease and the mean point estimate would become more precise. However, in specific situation the calculated z-value is far away from the rejection area. Thus, we don't need a larger sample size.

7. Conclusion

The new balls can be taken into production!

Appendix 1.

CurrentNew

264277

261269

267263

272266

258262

283251

258262

266289

259286

270264

263274

264266

284262

263271

260260

283281

255250

272263

266278

268264

CurrentNew

270272

287259

289264

280280

272274

275281

265276

260269

278268

275262

281283

274250

273253

263260

275270

267263

279261

274255

276263

262279

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