Histogram, box plot and hypothesis testing

  

Directions: Please complete the statistical analyses on that pages that follow for the sample data below. If you do the work for this project by hand, you must show the work you do to arrive at your results. If you use technology (Excel, graphing calculator, etc.) to obtain the results, you must state the technology you used to obtain the results.

Project Data: Lengths of 30 random rivers in the world measured in miles

   

431

800

485

 

500

800

309

 

926

790

618

 

383

375

605

 

425

380

531

 

538

434

300

 

540

800

420

 

301

659

865

 

360

512

424

 

338

430

652

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  

1. (10 points) Construct a grouped frequency distribution for the sample data. Use 6 classes. Use the minimum data value as the lower limit of the first class. 

  

Class

Limits

Class

Boundaries

Frequency

Relative

Frequency

Cumulative   Frequency

 

 

 

 

 

 

  

2. (3 points) Draw a histogram for the data set. Title the graph and label the axes appropriately.

3. (2 points) Does the distribution appear to be normal (yes or no)? Explain.  
4. (10 points) Find the following descriptive statistics for the sample data. 

  

Mean

Median

Mode(s)

 

   

Range

Standard   Deviation

 

  

5. (3 points) Find the quartiles for the data.

Q1 = _______________

Q2 = _______________

Q3 = _______________

6. (2 points) Sketch a box plot. Do your best to draw it to scale.

7. (2 point) What is the IQR for this data set? ____________

8. (3 points) Outlier identification 

Any value in this data set that is
less than ________ or greater than _______ is to be considered an outlier.

 

Therefore, the following values in this data set are outliers (write “none” if there are no outliers):

  

9. (3 points) Construct a 95% confidence interval for the population’s mean.

____________ < μ < ____________

10. (2 points) If someone were to ask you what this particular confidence interval means, what would you say?

  

11. (10 points) Test the hypothesis that the population’s mean is different from the sample’s median value. Use the traditional method. Use α = 0.05. 

Alternative hypothesis (H1): ________________

Null hypothesis (H0): _____________________

Critical value: ____________

Test statistic: ____________

Conclusion: 

Do you reject the null hypothesis (yes or no)? _________

If someone were to ask what the conclusion means in this particular study, what would you say?