Project One Traditional College Student Stress Scale complete solutions correct answers key

Project One

Traditional College Student Stress Scale  complete solutions correct answers key 

The life of a college student can be stressful. To gain an understanding of the stress level of college students a study was conducted. A random sample of 100 undergraduate college students attending a University on ground was given the “Traditional College Student Stress Scale.” They were not asked to return the form but only to anonymously submit the total score along with their age.  

*While it is not necessary to answer the questions below, you can access the Stress Scale questions in the “A Life Stress Instrument of Classroom Use” article, page 47.

Student Scores

Age

1299

21

1530

25

1449

18

1316

19

1613

19

1651

22

262

24

1258

23

829

25

718

21

1146

22

393

24

2279

18

1275

22

1093

22

543

23

2509

18

2144

25

1763

24

2179

22

1480

18

2233

18

1641

24

2407

18

2293

19

2218

19

529

21

1243

19

801

22

997

20

1892

21

2224

22

2056

21

2098

20

1428

24

2047

25

618

23

1774

22

2215

23

2432

21

196

22

1767

21

2149

19

914

21

1808

23

2423

22

1662

19

1795

22

312

21

949

23

854

23

2132

19

383

22

231

21

1897

18

2559

24

2106

18

1615

22

1438

23

1177

21

2358

24

1261

20

826

23

948

25

1343

25

1205

24

1990

23

447

21

547

18

1612

18

1324

24

1616

18

711

18

809

24

579

22

2275

24

1710

22

776

25

1859

19

824

19

2329

21

871

18

1377

25

651

18

997

22

1464

18

861

24

698

22

1367

23

1355

22

1931

18

2091

22

554

25

209

22

525

22

1908

21

536

22

1098

19

294

25

942

23

Answer the following questions

1.    Look at the manner in which the data was collected and identify any potential problems with using this as an evaluation tool.

2.    Find the Mean stress level of the sample.

Ans: 1373.2

3.    Find the Median stress level of the sample

Ans: 1361

4.    Find the Mode of the stress level for the students

Ans:997

5.    Find the Standard Deviation of the stress level for the random sample of 100 students

Ans:659.32923

6.    Find the Variance of the stress level for the random sample of 100 students.

Ans:434715.0303 (Standard Deviation) and 430367.88 (Population standard Deviation)

7.    Find the Range of the stress level of the 100 students.

Ans:2559-196=2363

8.    Create a Frequency Table for the stress level from the 100 college students. (Include classes, frequency, relative frequency, and cumulative frequency)

Ans:

9.    Using the Frequency table, create a Histogram of the stress levels from the sample of 100 college students.

10. Discuss the distribution of the data based on the histogram

Ans: This histogram reports that students at the age of 24 show a maximum level of stress while students at the age

11. Make a Scatter Plot of age vs. stress level. Do you see a trend?

12. Is there a linear correlation between the age of the student and the stress level? (Hint: Pearson’s Correlation Coefficient) Show your calculations.

Ans: Yes, there is a linear correlation as students reaching their last year of class tend to be more stressed than the ones that recent start. The plot shows that their level of stress is grater.

From our table:

•    Σx = 137320

•    Σy = 2149

•    Σxy = 3095410

•    Σx2 = 231604612

•    Σy2 = 46687

n is the sample size, in our case = 100

The correlation coefficient =

100(3095410) – (137320 × 2149) / [√[[100*231604612-(3095410)^2)] × [100*46687-(2149)^2]

=-0.209418336272343

13. Find the Least Squares Regression Line to fit the data displayed in the scatter plot from problem 11.

Ans:

The equation of the least squares regression line is:

y=b0 + b1*x

where b1 is the slope and b0 is the intercept (the point where the line crosses the y axis)

b0 =  = = 2687.001208

b1 = ==-61.1354680

Therefore, the regression line equation is :

y=2687.001208-61.1354680*x

14. Use the Least Square Regression line to find the stress level of a 25-year-old undergraduate.

Ans:

The regression line is

y=2687.001208-61.1354680*x

For x = 25, we have

y=2687.001208-61.1354680*25=1158.614508