Name: ______________________________ MAT 107 Project: Age of Students in College Professor Sumner Collect Data: (5 points) You will need to ask 30 college students their age. The students can attend any college or university. Use the table below to input the data you collected. If you do the work for this project by hand, you must show the work you do to arrive at your results to earn full credit. If you use technology (computer, calculator, etc.) to obtain the results, you must state the technology you used and describe how you used it to obtain the results to obtain full credit. The project is worth 40 points. 1. (5 points) Construct a grouped frequency distribution for the data. Use 5 classes and let the lower limit of the first class be the minimum data value. Class Limits Class Boundaries Frequency Relative Cumulative Frequency Frequency 2. (2 points) Construct a histogram for the data set. Be sure to label the axes appropriately. 3. (1 point) Comment on the shape of the distribution. Does it appear to be symmetric, uniform, skewed left, or skewed right? Refer to page 73 in Section 2.3 of the textbook. 4. (6 points) Find the following descriptive statistics for the sample data. Mean Median Mode Range Variance Standard Deviation 5. (5 points) Find the five-number summary for the data. Min = ______________________ Max = ______________________ Q1 = _______________________ Q2 = _______________________ Q3 = _______________________ 6. (1 point) Sketch a boxplot of the data. 7. (1 point) What is the IQR? __________________ 8. (3 points) Identify any outliers using the technique described near the bottom of page 104 in Section 2.5 of the textbook. Any data value less than ______________ or greater than______________ is to be considered an outlier. Therefore, the following data values are outliers (write \"none\" if there are no outliers): 9. (1 point) What is the z-score for a student that is 18 years old? z = ____________ 10. (1 point) What is the z-score for a student that is 37 years old? z = ____________ 11. (1 point) If someone were to ask you what the z-score for 18 years old means, what would you say? 12. (1 point) Construct a 95% confidence interval for the population's mean age. _______________ < < ________________ 13. (1 point) If someone were to ask you what this particular confidence interval means, what would you say? 14. Test the hypothesis that the population's mean age is greater than 26. Use = 0.05. (1 point) Null hypothesis (H0): ______________________________ (1 point) Alternative hypothesis (Ha): _________________________ (1 point) Test statistic (z-test): _____________________________ (1 point) p-value: _____________________________ (1 point) Conclusion: Do you reject the null hypothesis? (yes or no) ________________________ (1 point) If someone were to ask what the conclusion means in this particular situation, what would you say