mathexpert published posts

Doing Independent-Samples T-tests

  1. Download the file timeonsite.csv from the course materials. This file describes a website A/B test in which visitors’ time-on-site was measured in two website variations. How many subjects were in this website A/B test?
  2. How many subjects were exposed to each variation of the website A and B?
  3. To the nearest tenth (one digit), what was the median time on sire for site “B”?
  4. To the nearest hundredth (two digits), what was the standard deviation of time on site for site “A”?
  5. Conduct an independent-samples t-test on Time by Site. Assume equal variances. To the nearest hundredth (two digits), What is the t-statistic?
  6. How many degrees of freedom resulted from the t-test?
  7. To the nearest ten-thousandth (four digits), what was the p-value for this test?
  8. What is the most proper way to report this t-test result?
  9. The results show that, on average, website “A” resulted in almost 13 seconds greater time-on-sire than website “B”, and that this difference was statistically significant. (Note: Assume Time is measured in seconds).
  10. By Setting the var. equal parameter to FALSE, a Welch t-test can be run, which does not assume equal variances.

Understanding Experiment Designs

  1. What might account for random error in an experimental measure?

    • natural variation among and within subjects
    • A systematic flaw in the logging software
    • A pattern of dropped data for every fifth subject
    • Biased observations
  2. Which of the following would be an ordinal response? (Mark all tha apply)

    • Responses on a Likert-type scale
    • Height in centimeters of each subject
    • Favorite color of each subject
    • How spicy each subject prefers their Thai food using 1-5 stars

      • The number of heads resulting from one-hundred coin flips
  3. In an experiment, factors are the independent variables manipulated by the experimenter, and level are the specific values a factor can take on.

    • True
    • False
  4. A between-subjects factor is most precisely defined by which of the following characteristic?

    • Each subject experiences more than one level of the factor
    • Each subject experiences only one level of the factor,
    • Each subject experiences all levels of the factor.
    • Each subject experiences all but one level of the factor.
    • None of the above
  5. A within-subjects factor is most precisely defined by which of the following characteristic?

    • Each subject experiences more than one level of the factor.
    • Each subject experiences only one level of the factor,
    • Each subject experiences all levels of the factor.
    • Each subject experiences all but one level of the factor.
    • None of the above
  6. If a given factor has four levels and subjects experience two of the four levels, that factor is most precisely described as:

    • A within-subjects factor
    • A between-subjects factor
    • A partial within-subjects factor
    • A partial between-subjects factor
    • None of the above
  7. Balanced experimental designs are where every subject experiences every level of every factor

    • True
    • False
  8. The most common use of an independent-samples t-test is to examine which of the following?

    • One set of subjects that all does the same thing
    • One set of subjects that does two different things
    • Two sets of subjects that do the exact same thing
    • Two sets of subjects that do different things
    • None of the above
  9. Which of the following is the most proper way to report a t-test result?

    • t(14) = 2.76. p = .015
    • t(14) = 2.76, p < .05
  10. A t-test is a test suited to one factor with two levels

    • True
    • False


Your company is running a Medicare audit on Sleaze Hospital. Because Sleaze has a history of overbilling, the focus of your audit is on checking whether the billing amounts are correct. Assume that each invoice is for too high an amount with probability 0.06 and for too low an amount with probability 0.01 (so that the probability of a correct billing is 0.93). Also, assume that the outcome for any invoice is probabilistically independent of the outcomes for other invoices.

For this Assignment, reflect on the case presented. Think about what strategies you might use to calculate associated probabilities for Sleaze Hospital, and then address the series of questions for the completion of the Assignment.


If you randomly sample 200 of Sleaze's invoices, what is the probability that you will find at least 15 invoices that overcharge the customer? What is the probability you won't find any that undercharge the customer?

Find an integer, k, such that the probability is at least 0.99 that you will find at least k invoices that overcharge the customer. (Hint: Use trial and error with the BINOMDIST function to find k.)

Suppose that when Sleaze overcharges Medicare, the distribution of the amount overcharged (expressed as a percentage of the correct billing amount) is normally distributed with mean 15% and standard deviation 4%.

What percentage of overbilled invoices are at least 10% more than the legal billing amount?

What percentage of all invoices are at least 10% more than the legal billing amount?

If your auditing company samples 200 randomly chosen invoices, what is the probability that it will find at least five where Medicare was overcharged by at least 10%?

Submit your answers and embedded Excel analysis as a Microsoft Word management report.


Albright, S. C., & Winston, W. L. (2017). Business analytics: Data analysis and decision making (6th ed.). Stamford, CT: Cengage Learning.

Chapter 4, "Probability and Probability Distributions"
Chapter 5, "Normal, Binomial, Poisson, and Exponential Distributions"
Fulton, L. V., Mendez, F. A., Bastian, N. D., & Musal, R. M. (2012). Confusion between odds and probability, a pandemic? Journal of Statistics Education, 20(3), 1–20.
Note: Retrieved from the Walden Library databases.Microsoft. (2016). Statistical functions (reference).Links to an external site. Retrieved from


As you have examined this week, healthcare administration leaders are expected to exercise decision making under conditions of uncertainty. Perhaps more so than any other business, healthcare administration leaders face multiple challenges since ineffective business practices might not result in poor performance with their bottom lines and, if not, it might negatively impact patient safety. Understanding how to appropriately exercise decision making under conditions of uncertainty is a useful skill for effective healthcare administration practice.

For this Assignment, review the resources for this week, and reflect on how healthcare administration leaders must exercise decision making under conditions of uncertainty. Consider how you might engage in decision making under uncertainty, as you complete the Assignment and the Case Study 6.4 on pages 275-276 of your course text. Note: You will need to use Excel and the textbook add-in, "Precision Tree."

Alternatively, you may also download the PrecisionTree software as a Free Trial by accessing the following: to an external site.

You will need to fill out the information presented and will need to use a personal email address to use the Free Trial provided.


The Ventron Engineering Company has just been awarded a $2 million development contract by the U.S. Army Aviation Systems Command to develop a blade spar for its Heavy Lift Helicopter program. The blade spar is a metal tube that runs the length of and provides strength to the helicop- ter blade. Due to the unusual length and size of the Heavy Lift Helicopter blade, Ventron is unable to produce a single-piece blade spar of the required dimensions using existing extrusion equipment and material. The engineering department has prepared two alternatives for developing the blade spar: (1) sectioning or (2) an improved extrusion process. Ventron must decide which process to use. (Backing out of the contract at any point is not an option.) The risk report has been prepared by the engineer- ing department. The information from this report is explained next.

The sectioning option involves joining several shorter lengths of extruded metal into a blade spar of sufficient length. This work will require extensive testing and rework over a 12-month period at a total cost of $1.8 million. Although this process will definitely produce an adequate blade spar, it merely represents an extension of existing technology. To improve the extrusion process, on the other hand, it will be necessary to perform two steps: (1) improve the material used, at a cost of $300,000, and (2) modify the extrusion press, at a cost of $960,000. The first step will require six months of work, and if this first step is successful, the second step will require another six months of work. If both steps are successful, the blade spar will be available at that time, that is, a year from now. The engineers estimate that the probabilities of succeeding in steps 1 and 2 are 0.9 and 0.75, respectively. However, if either step is unsuccessful (which will be known only in six months for step 1 and in a year for step 2), Ventron will have no alternative but to switch to the sectioning process—and incur the sectioning cost on top of any costs already incurred.

Development of the blade spar must be com- pleted within 18 months to avoid holding up the rest of the contract. If necessary, the sectioning work can be done on an accelerated basis in a six-month period, but the cost of sectioning will then increase from $1.8 million to $2.4 million. The director of engineering, Dr. Smith, wants to try developing the improved extrusion process. He reasons that this is not only cheaper (if successful) for the current proj- ect, but its expected side benefits for future projects could be sizable. Although these side benefits are dif- ficult to gauge, Dr. Smith’s best guess is an additional $2 million. (These side benefits are obtained only if both steps of the modified extrusion process are completed successfully.)

a. Develop a decision tree to maximize Ventron’s EMV. This includes the revenue from this project, the side benefits (if applicable) from an improved extrusion process, and relevant costs. You don’t need to worry about the time value of money; that is, no discounting or net present values are required. Summarize your findings in words in the spreadsheet.

b. What value of side benefits would make Ventron indifferent between the two alternatives?

c. How much would Ventron be willing to pay, right now, for perfect information about both steps of the improved extrusion process? (This information would tell Ventron, right now, the ultimate success or failure outcomes of both steps.

You may use whatever method you prefer to complete the assignment (i.e. could be done in Excel, Jupyter Notebook, Tableau, etc.).

  1. The deliverable should be an email with findings from your work. Include screenshots of tables, charts, etc. to help tell the story. Additionally, attach any code you wrote.


  1. Forecast the YoY performance of three restaurant chains: EAT (period ending 12/23/2020), DRI (period ending 11/29/2020), and TXRH (period ending 12/29/2020) using the provided transaction data. The data to complete the request can be found in the “Case Study Data.xlsx” file.
  2. Write the SQL queries you would have used to calculate the quarterly YoY % changes in each of the restaurant chain’s transaction data.
  3. Use the Review Data to formulate an opinion on the quality of each restaurant chain.
  4. Tell us if you think there is any fundamental characteristics that separate one of these chains from the others. Tell us if you feel there is any reason to invest or why not to invest in any of these chains. Feel free to research and contemplate each chain’s position within broader secular changes.

Assignment Data file