BUSI 275 Fall 2011 Midterm Exam Practise Questions

[ answers in web view ]
As an aid for your study, here are a collection of questions similar to what might show up on the midterm exam. The actual exam may be longer or shorter, there may be some material on the exam that is not covered here, and there may be some material here that doesn't show up on the exam. The coverage for the exam is ch1-8 in our textbook.
The exam is in-class, 70min long, and you will enter your answers on the computer. You may use Excel, the lecture notes, textbook, and any resource on the Internet that is not a live person. You may not communicate in any way (including text message, email, chat, etc.) with classmates or anyone outside of class; if you have a question, raise your hand and I will help you as much as I can.
  1. A quality control inspector has rated each batch produced today on a scale from A through E, where A represents the best quality and E is the worst. What is the level of measurement of this variable?
  2. Your customers’ average order size is $2601, with a standard deviation of $1275. Suppose 45 typical customers independently placed orders tomorrow. What are the chances that tomorrow’s average order per customer will be between $2450 and $2750?
    SE=190, z = -0.7945 and +0.7839, so area in between is 57%
  3. Using the information in the preceding problem, produce a 95% confidence interval on average order per customer per day, assuming 20 customers per day.
    SE=285.10, z = +/- 1.96, so conf. int. is between $2042.22 and $3159.78.
  4. The table below shows sales of some “light” foods:
    "Light" Food Sales ($Millions)
    Entenmann's Fat Free baked goods $125.5
    Healthy Request soup $123.0
    Kraft Free processed cheese $83.4
    Aunt Jemima Lite and Butter Lite pancake syrup $58.0
    Fat Free Fig Newtons $44.4
    Hellmann's Light mayonnaise $38.0
    Louis Rich turkey bacon $32.1
    Kraft Miracle Whip free $30.3
    Ben & Jerry's frozen yogurt $24.4
    Hostess Lights snack cakes $19.3
    Perdue chicken/turkey franks $3.8
    Milky Way II candy bar $1.1
    My company is planning to launch a new brand of light food. Our goal is to reach at least the 20th percentile of current brands. What is our sales goal, in dollars?
    rank=2.4, round up to 3: 3rd entry is $19.3.
    Or, using PERCENTILE(): $20.32.
    The difference is due to the different way Excel computes percentiles.
  5. Produce a relative frequency histogram for the variable "Airline" in the dataset AirlinePassengers.xls (linked).
  6. Using the same dataset from the preceding problem, produce a joint frequency distribution for the two variables, "Male/Fem." and "Business or Pleasure". Are these two variables independent in this dataset? Why or why not?
    No: e.g., P(Business | Male) ≠ P(Business | Female)
  7. You have followed up on people who received your catalog mailing. You found that 4% of these people ordered the hat, and 6% ordered the mittens. Of the people who ordered the hat, 55% also ordered the mittens. Of the people who did not order the hat, what percentage ordered the mittens?
    Given: P(H)=4%, P(M)=6%, P(M|H)=55%, the question is looking for P(M|noH).
    Then P(M and H) = (.04)(.55) = 2.2%.
    Since P(M and H) and P(M and noH) must add up to P(M), so P(M and noH) must equal 6% - 2.2% = 3.8%.
    We are looking for P(M|noH), which is P(M and noH) / P(noH).
    P(noH) must be 100% - P(H) = 96%, so
    P(M|noH) = 3.8% / 96% = 3.958333%.
  8. Here are the satisfaction scores given by 12 randomly selected customers:
    89 98 96 65 99 81 76 51 82 90 96 76
    Does the observed average differ significantly from the target score of 80?
    mean = 83.25, SD = 14.63, SE = 4.223.
    z = (80-83.25)/SE = -0.77, % area in left tail = 22.08%.
    No, does not significantly differ (technically, this question is a ch9 question if we consider an α, but the components are within ch7-8).
  9. In a nationwide poll for a political candidate, we found that 309 out of 1105 registered voters claimed to be in favor of that candidate. If we report our findings with 95% confidence, what is our margin of error?
    SE = 1.3502%, z=1.96, so margin of error (the +/- in the confidence interval) is just (1.96)(1.3502%) = 2.65%
  10. In order to pay your firm’s debts this year, you will need to be awarded at least 2 contracts. This is not usually a problem, since the yearly average is 5.1 contracts. What is the probability that you will not earn enough to pay your firm’s debts this year? (Hint: which distribution is appropriate?)
    POISSON(1, 5.1, 1) = 3.72%
  11. Your client has a particularly complex database procedure it needs to run quickly. Your company can provide a new computer system to speed it up. You have run the procedure on your new system 14 times (independent runs) and obtained the following runtimes (in minutes):
    5 8 5 6 11 9 8 10 5 11 6 5 5 10
    You would like to claim that your new system is very fast. In your advertising, you will say, "average processing time is as low as ___". Find the appropriate bound of the two-sided 95% confidence interval.
    t-score is TINV(.05,13) = 2.16.
    mean = 7.43, sd = 2.41, SE = 0.6438.
    Conf int is 6.038 to 8.819 (we want the lower bound).
  12. You would like to estimate the average price of a stock to a precision of +/- 1%, with 95% confidence. Assume the volatility (coefficient of variation) of the stock is 12%. Assuming each day's price is independent and normally distributed, how many days should you track the stock in order to attain this precision in estimating its average price?
    SD = 0.12μ, so SE = 0.12μ/sqrt(n).
    Margin of error = 0.01μ.
    95% confidence implies a z-score of NORMSINV(0.975) = 1.96, so
    1.96 = 0.01μ / (0.12μ / sqrt(n)).
    Solving for n: n = ( (1.96)(0.12)/(0.01) )2 = 554
  13. (p.255 #41) The mean time between failures (MTBF) for a particular model of power supply unit (PSU) is 4,000 hours. Some PSUs may fail earlier; some later. What is the probability of a random PSU failing in less than 2,100 hours? (Hint: which probability distribution is appropriate?)