MAT 107 Differential Statistics Problems

Name: ______________________________MAT 107
Project
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
500
926
383
425
538
540
301
360
338
800
800
790
375
380
434
800
659
512
430
485
309
618
605
531
300
420
865
424
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 Cumulative
Frequency Frequency
2. (3 points) Draw a histogram for the data set.
graph and label the axes appropriately.
Title the
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
Range
Mode(s)
Standard Deviation
5. (3 points) Find the quartiles for the data.
Q1 = _______________
Q2 = _______________
Q3 = _______________
6. (2 points) Sketch a box plot.
scale.
Do your best to draw it to
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?