You are the Director of Human Resources for a Gym.You want to increase the usage of the facility among the existing members belonging to a category i.e. working in jobs which require high fitness standards (e.g. models, pilots, industry plant workers etc). You want to gather some inferential statistics about your gym member's income.You also wish to determine if such gym member's usage of the facility per week is useful for predicting the income (in $) of gym member.

THE DATA:The Gym usage per week of 180 randomly selected members are listed below.For linear regression, the X-variable is the Gym usage per week, and the Y-variable is Income.

ROUND OFF ALL CALCULATIONS TO AT LEAST FOUR DECIMAL PLACES.Highlight the cells with output where decimal places need setting.Then use the "Increase Decimal" tool on Excel's Home/Number menu to four decimal places.

3.Assume that the population standard deviation is 0.30 and assume the population is approximately normally distributed.Find the sample size that would be required to determine a 95% confidence interval for the true mean income of gym members if we want to be within 0.10 of the true mean. That is, we want the margin of error, e, to not exceed 0.10.

INSTRUCTIONS:Answer all the questions below. All calculations must be performed with Excel or PHStat. Attach Excel or PHStat output where indicated.

Gym Usage per week (X) Income (in $) (Y)

3 29562

2 31836

4 30699

3 32973

4 35247

3 32973

3 35247

3 32973

5 35247

2 37521

3 36384

3 35247

4 36384

3 35247

3 38658

3 40932

2 34110

4 39795

4 38658

2 34110

4 38658

4 40932

4 42069

5 44343

2 45480

3 42069

4 46617

3 48891

2 45480

2 53439

3 39795

3 40932

2 40932

3 43206

3 44343

4 52302

2 53439

3 51165

3 36384

4 44343

3 50028

3 45480

4 54576

2 45480

2 46617

2 52302

3 52302

3 54576

4 54576

3 51165

3 68220

2 46617

4 50028

4 46617

3 54576

2 54576

2 45480

3 46617

4 52302

2 55713

3 46617

4 51165

2 52302

4 48891

3 60261

3 67083

4 44343

3 37521

3 46617

2 54576

2 52302

3 56850

4 59124

3 61398

4 54576

3 53439

3 57987

3 60261

4 56850

3 64809

3 31836

2 32973

3 34110

3 38658

5 34110

2 34110

2 32973

3 36384

3 38658

3 45480

4 45480

3 43206

3 40932

3 45480

3 40932

3 48891

3 50028

2 45480

3 43206

2 52302

5 47754

3 45480

2 43206

4 45480

3 43206

2 50028

2 45480

4 48891

4 45480

4 50028

4 51165

4 45480

3 51165

3 57987

4 46617

3 52302

2 51165

2 65220

4 60261

3 53439

4 53439

2 50028

3 51165

5 53439

3 47754

4 64809

3 59124

3 67083

3 52302

3 53439

3 50028

3 53439

2 48891

4 62535

3 59124

3 61398

3 57987

3 64809

2 54576

2 57987

4 48658

3 54781

4 48556

4 58516

5 53536

4 48556

4 61006

4 57271

5 52291

5 49801

4 49801

4 62251

5 61006

4 64741

6 70966

6 75946

4 74701

4 69721

5 64741

4 83416

4 88396

4 90886

6 92131

7 77191

6 88396

5 52290

7 85906

6 90886

5 103336

5 99601

6 89641

4 95866

5 92131

4 92131

5 104581

6 83416

5 89641

5 90886

4 104581

4 95508