Practice Set 02

Remarks on hypothesis testing exercises

  1. It is important to think carefully about what are the “ordinary” and “out-of-ordinary” claims. Make sure to state what these are in different ways – vary the level of sophistication of how you write these claims. But maintain communication accuracy.

  2. Formulate the R code necessary to produce results for making a decision.

  3. Express and communicate your finding to decision makers and/or stakeholders without reference to \(p\)-values and other jargon.

Exercise: Drug effectiveness

Recent medical research has sought to develop drugs that lessen the severity and duration of viral infections. A relatively new drug called Virol has been shown to provide relief for 70 percent of all patients suffering from viral upper respiratory infections. A major drug company is developing a competing drug called Panatol. The drug company wishes to investigate whether Phanatol is more effective than Virol. Three hundred patients with viral upper respiratory infections were randomly selected and 231 of these patients were provided relief by Phanatol. What course of action would you recommend to the company taking the evidence and the situation as given?

Exercise: Cheese spreads

A food processing company markets a soft cheese spread that is sold in a plastic container with an “easy pour” spout. Although this spout works extremely well and is popular with consumers, it is expensive to produce. While the new, cheaper spout may alienate some purchasers, the company has an internal calculation suggesting that introducing the new, cheaper spout will increase profits if fewer than 10 percent of the cheese spread’s current purchasers are lost. Suppose that after trying the new spout, 63 out of 1000 randomly selected purchasers say that they would stop buying the cheese spread if the new spout were used. What course of action would you recommend to the company taking the evidence and the situation as given?

Exercise: Electronic article surveillance

A sports equipment discount store is considering installing an electronic article surveillance device and is concerned about the proportion of all consumers who would never shop in the store again if the store subjected them to a false alarm. Suppose that industry data for general stores say that 15 percent of all consumers state that they would never shop in a store again if the store subjected them to a false alarm. The store randomly selected 500 consumers and found that 70 out of the 500 consumers stated they would never shop in the store again if the store subjected them to a false alarm. What course of action would you recommend to the company taking the evidence and the situation as given?

Exercise: Marketing mouthwash

An ad agency has developed a TV ad for the introduction of the mouthwash. The objective of the ad is to create awareness of the brand. The objective of this research is to evaluate awareness generated by the ad measured by unaided recall scores. In order for the ad to be considered successful, the percentage of unaided recall must be above the category norm for a TV commercial for the product class which is 18 percent. A minimum of 200 respondents who claim to have watched the TV show in which the ad was aired the night before will be contacted by telephone in 20 cities. Suppose a random sample of 200 respondents shows that 46 of the people interviewed were able to recall the commercial without any prompting. What course of action would you recommend to the company taking the evidence and the situation as given?

Exercise: Reflection

  1. What do you notice about the exercises? Do you see patterns in the descriptions?
  2. A lot of assumptions is hidden in the way the hypothesis testing argument was introduced to you. Examine the exercises here and those found in the slides more carefully. How do you think the data were obtained? What assumptions do we have to make? How are the R codes reflective of those assumptions?
  3. Reflect also on the how you used a \(p\)-value to make recommendations. What \(p\)-value is large for you? small for you?
  4. When recommending courses of action or communicating what the evidence shows, do you think it is possible to make mistakes? Why or why not?

Remarks on decision-making under uncertainty

  1. These exercises are about modifying the R code in the slides to reflect a new situation or to revisit an old situation.
  2. Just like the hypothesis testing case, the simulations relied on assumptions too.

Exercise: Revisiting firm entry

You saw two versions of the firm entry case. Do this exercise for both versions.

  1. Run the code on your own computer a few times. What do you notice about the patterns of your outputs compared to the slides.

  2. Answer the following questions:

    1. The “long-run” average profits for next year
    2. The “long-run” standard deviation of profits next year
    3. How likely is it that firm’s profit next year will be negative
    4. The “long-run” median level of the firm’s profit next year
    5. The level of the firm’s profit next year that has cumulative probability 0.75
    6. The level of the firm’s profit next year that has cumulative probability 0.05

Exercise: Laser pointers

The Feline Company has substantial uncertainty about many factors that will affect its profit from selling laser pointers next year. Feline’s director of marketing estimates that the total demand for laser pointers (sold by all firms in the market) may be 60,000 or 70,000 or 80,000 laser pointers next year, and the probabilities of these three possibilities are 0.2, 0.6, and 0.2, respectively. Feline’s share of this total market for laser pointers next year may be 0.15 or 0.20 or 0.25 or 0.30, with probabilities 0.2, 0.3, 0.3, and 0.2, respectively. The price of laser pointer next year may be $ 90 or $ 100 or $ 110 per laser pointer, with probabilities 0.2, 0.7, and 0.1, respectively.

  1. Modify the code found in the slides to reflect this new situation. You have to define what profits look like in this case.

  2. Modify the R code so that you can use the simulation data to estimate:

    1. The “long-run” average profits for next year
    2. The “long-run” standard deviation of profits next year
    3. How likely is it that Feline’s profit next year will be negative
    4. The “long-run” median level of Feline’s profit next year
    5. The level of Feline’s profit next year that has cumulative probability 0.75
    6. The level of Feline’s profit next year that has cumulative probability 0.05