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Chapter 8: Q89E (page 452)
Find a value of the standard normal random variable z, call it , such that
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Last name and acquisition timing. Refer to the Journal of Consumer Research (August 2011) study of the last name effect in acquisition timing, Exercise 8.13 (p. 466). Recall that the mean response times (in minutes) to acquire free tickets were compared for two groups of MBA students— those students with last names beginning with one of the first nine letters of the alphabet and those with last names beginning with one of the last nine letters of the alphabet. How many MBA students from each group would need to be selected to estimate the difference in mean times to within 2 minutes of its true value with 95% confidence? (Assume equal sample sizes were selected for each group and that the response time standard deviation for both groups is ≈ 9 minutes.)
Oil content of fried sweet potato chips. Refer to theJournal of Food Engineering (September 2013) study of the characteristics of fried sweet potato chips, Exercise 7.90 (p. 431). Recall that a sample of 6 sweet potato slices fried at 130° using a vacuum fryer yielded the following statistics on internal oil content (measured in gigagrams [Gg]): x1 = .178 Gg and s1 = .011 Gg. A second sample of 6 sweet potato slices was obtained, but these were subjected to a two-stage frying process (again, at 130°) in an attempt to
improve texture and appearance. Summary statistics on internal oil content for this second sample follows: x2 = .140 Gg and s2 = .002 Gg. Using a t-test, the researchers want to compare the mean internal oil content of sweet potato chips fried with the two methods. Do you recommend the researchers carry out this analysis? Explain.
Predicting software blights. Relate to the Pledge Software Engineering Repository data on 498 modules of software law written in “C” language for a NASA spacecraft instrument, saved in the train. (See Exercise 3.132, p. 209). Recall that the software law in each module was estimated for blights; 49 were classified as “true” (i.e., the module has imperfect law), and 449 were classified as “false” (i.e., the module has corrected law). Consider these to be Arbitrary independent samples of software law modules. Experimenters prognosticated the disfigurement status of each module using the simple algorithm, “If the number of lines of law in the module exceeds 50, prognosticate the module to have a disfigurement.” The accompanying SPSS printout shows the number of modules in each of the two samples that were prognosticated to have blights (PRED_LOC = “yes”) and prognosticated to have no blights (PRED_LOC = “no”). Now, define the delicacy rate of the algorithm as the proportion of modules. That was rightly prognosticated. Compare the delicacy rate of the algorithm when applied to modules with imperfect law with the delicacy rate of the algorithm when applied to modules with correct law. Use a 99-confidence interval.
DEFECT*PRED_LOC crosstabulation
| PRED_LOC | total | ||
| no | yes | ||
DEFECT False True total | 440 29 429 | 49 20 69 | 449 49 498 |
Optimal goal target in soccer. When attempting to score a goal in soccer, where should you aim your shot? Should you aim for a goalpost (as some soccer coaches teach), the middle of the goal, or some other target? To answer these questions, Chance (Fall 2009) utilized the normal probability distribution. Suppose the accuracy x of a professional soccer player’s shots follows a normal distribution with a mean of 0 feet and a standard deviation of 3 feet. (For example, if the player hits his target,x=0; if he misses his target 2 feet to the right, x=2; and if he misses 1 foot to the left,x=-1.) Now, a regulation soccer goal is 24 feet wide. Assume that a goalkeeper will stop (save) all shots within 9 feet of where he is standing; all other shots on goal will score. Consider a goalkeeper who stands in the middle of the goal.
a. If the player aims for the right goalpost, what is the probability that he will score?
b. If the player aims for the center of the goal, what is the probability that he will score?
c. If the player aims for halfway between the right goal post and the outer limit of the goalkeeper’s reach, what is the probability that he will score?
Question: Deferred tax allowance study. A study was conducted to identify accounting choice variables that influence a manager’s decision to change the level of the deferred tax asset allowance at the firm (The Engineering Economist, January/February 2004). Data were collected for a sample of 329 firms that reported deferred tax assets in 2000. The dependent variable of interest (DTVA) is measured as the change in the deferred tax asset valuation allowance divided by the deferred tax asset. The independent variables used as predictors of DTVA are listed as follows:
LEVERAGE: x1= ratio of debt book value to shareholder’s equity
BONUS: x2 = 1 if firm maintains a management bonus plan,
0 if not
MVALUE: x3 = market value of common stock
BBATH: x4 = 1 if operating earnings negative and lower than last year,
0 if not
EARN: x5 = change in operating earnings divided by total assets
A first-order model was fit to the data with the following results (p-values in parentheses):
Ra2 = .280
(.070) (.228) (.157) (.678) (.001) (.869)
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