The statistical analyses
Complete the statistical analyses 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.
AlternatZve 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?
