answer the following questions using the following:

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

4.Using your sample data ( the data above), test this hypothesis at the alpha = 0.01 significance level.You may assume that the population standard deviation is not known and that the population is approximately normally distributed.

(a)Is there sufficient evidence to conclude that the mean income for all such gym members is more than 90000?

PASTE PHSTAT OUTPUT BELOW:

(b)Test the hypothesis again, changing alpha to 0.05 but not changing anything else.

PASTE PHSTAT OUTPUT BELOW:

Now mark all of the following statements about the two hypothesis tests either T(TRUE) or F(FALSE).

____ The p-value is the probability that the null hypothesis will be rejected.

_____ The second test has a smaller "reject" region than the first.

_________The test statistic measures the distance between the mean being tested and the sample mean.

______ The null hypothesis will be rejected provided alpha exceeds the p-value.

_________The critical value is the boundary between the "reject" region and the "do not reject" region.

_________The p-value is the probability of getting a test statistic equal to, or more extreme than the sample result, if the null hypothesis is true.