1. An experiment was conducted to measure the effect of popcorn brand on the yield (in cups of
    popper popcorn from ¼ cup of popcorn). The brands are Gourmet, National, and Generic
    Brand. The obtained data are as follows:
    Brand
    Gourmet National Generic
    5.5 4.5 3.5
    5.5 4.5 4
    6 4 3
    6.5 5 4
    7 5.5 5
    7 5 4.5
    Mean 6.25 4.75 4 Overall = 5
    Standard Deviation 0.6892 0.5244 0.7071
    Does popcorn brand significantly impact popcorn yield at 5% significance level?
    (10 marks)
  2. An experiment was conducted to measure the effect of popcorn brand as well as the type of
    popcorn maker/popper and their interactions on the yield (in cups of popper popcorn from ¼
    cup of popcorn). The types of poppers used in the tests were Oil-based versus Air-based.
    And, the popcorn brands were Gourmet, National, and Generic Brand. The obtained data are
    as follows. Do type of popcorn maker and popcorn brand and their interactions significantly
    impact popcorn yield at 5% significance level? (15 marks)
    Brand Row mean Popper Gourmet National Generic
    Oil-based 5.5 4.5 3.5
    5.5 4.5 4
    6 4 3
    mean 17/3 13/3 10.5/3 4.5
    Air-based 6.5 5 4
    7 5.5 5
    7 5 4.5
    mean 20.5/3 15.5/3 13.5/3 5.5
    Column Mean 6.25 4.75 4 Overall = 5
    Carleton University – Faculty of Engineering
    ECOR 2050
    Instructor: S. Shams Assignment #5 Due: Fri. Dec 10, Midnight
    SHOW ALL CALCULATIONS & CLEARLY STATE ASSUMPTIONS & CONCLUSIONS!
  3. You are curious to understand if a woman’s height (cm) can be used as a predictor of her
    shoe size (in Canada/US scale, that is usually measured as 4 to 16).
    You are limited to collect 7 sets of data (shoe size vs height) from 7 women.
    a) Collect the information and record them in the table below (please use a typed
    table/numbers as we need to copy/paste your numbers into Excel for checking your
    solution and marking). Mention how you ensured that your data set is random and
    unbiased. (4 marks)
    Person 1 2 3 4 5 6 7
    Height (cm)
    Shoe size (US scale)
    b) Using the collected information, conduct a simple linear regression analysis and find the
    regression line. (8 marks)
    c) Estimate the coefficient of determination of the regression and explain what it indicates.
    (3 marks)
    d) Conduct an ANOVA diagnostics for the regression and explain what it indicates. Does it
    approve the finding of part c? (8 marks)
    e) If a woman’s height is 160 cm, What is the 95% confidence interval for her shoe size?
    (7 marks)

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