Unit Operations Laboratory 1

Statistics Homework

ChEn 475 – Knotts Name:

  1. (2 points) Explain what is meant by vs and vs .
  2. (5 points) Explain what is meant by sample vs population when calculating the standard deviation. Which is usually used in engineering practice and why?
  3. (3 points) List all of the functions to calculate the standard deviation, both population and sample, in Excel and Mathcad. Make sure to include the deprecated ones.
  4. (5 points) Explain the difference between a 95% confidence interval and .
  5. (6 points) What happens to as you increase the number of data points you take? What happens to the 95% confidence interval as you take more data? Explain why these behaviors occur.
  6. (4 points) What is ? How is it used?
  7. (5 points) What is the difference between one tail and two tail distributions? How do you know which to use?
  8. (4 points) Why is the Student’s T distribution wider than the normal distribution?
  9. (6 points) Imagine you measured 10 data points for the vapor pressure of hexane at 280 K. Calculate the value of that you would use to determine the 99% confidence interval in the following ways. (Note: you should get the same numerical value in each case)
  10. The Excel function tinv (show the formula and the final answer).
  11. The Excel function t.inv (show the formula and the final answer).
  12. The Excel function t.inv.2t(show the formula and the final answer).
  13. The table found at
  14. Table 2 in the following
  15. An appropriate Mathcad function.
  16. (4 points) Why did this assignment require you to do 9a-9c? 9d-9e? (Why the repetition?)
  17. (7 points) You made the following measurements for the normal boiling point of acetone (in K).

330

329

329

328

335

326

What will you report the normal boiling point as and what uncertainty will you assign to the value?

  1. (5 points) To double-check your work, a colleague performs the same experiment to measure the normal boiling point of acetone and obtains the following data (in K).

329

338

322

330

320

335

Are the data consistent with what you expect from your experiment? Explain.

  1. (7 points) The following data have been measured for the free convective heat transfer coefficient (W m-2 K-1) in the UO Lab.

20

17

24

30

10

Calculate a 99.7% confidence interval for the true mean free convective heat transfer coefficient.

  1. You have measured the following data for the liquid heat capacity (Cp) of o,p-bisphenol a.

T / Cp
(K) / (J mol-1 K-1)
384 / 544
424 / 588
450 / 611
489 / 639
502 / 647
529 / 662
542 / 672
568 / 689
607 / 704
634 / 714
  1. (3 points) Fit these data to an appropriate model and report the model.
  2. (4 points) Give evidence that the data do or do not fit the model.
  3. (8 points) Report the values of the model parameters along with their respective 95% confidence intervals and units.
  4. (2 points) Create a graph showing the data as points and the best-fit model as a line.
  5. (8 points) On your same graph, show 1) 95% prediction bands (single point prediction band) and 2) 95% confidence intervals (mean prediction band). Make sure to label them accordingly. Explain, in your own words, the difference between the two.(Note: This terminology can be tricky. Some textbooks use the opposite terminology. Either way, you should be able to explain in your words, what each is and avoid confusion.)
  6. (3 points) What is the value (and associated error) for Cp at T = 470 K.

ChEn 475 – KnottsPage 1 of 2Stats HW