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Chapter 8: Q158SE (page 452)
Consider the discrete probability distribution shown here.
x | 10 | 12 | 18 | 20 |
p | .2 | .3 | .1 | .4 |
a. Calculate and .
b. What is ?
c. Calculate .
d. What is the probability that xis in the interval ?
(a)
(b)
(c)
(d) The required probability is 0.5.
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Bankruptcy effect on U.S. airfares. Both Delta Airlines and USAir filed for bankruptcy. A study of the impact of bankruptcy on the fares charged by U.S. airlines was published in Research in Applied Economics (Vol. 2, 2010). The researchers collected data on Orlando-bound airfares for three airlines—Southwest (a stable airline), Delta (just entering bankruptcy at the time), and USAir (emerging from bankruptcy). A large sample of nonrefundable ticket prices was obtained for each airline following USAir’s emergence from bankruptcy, and then a 95% confidence interval for the true mean airfare was obtained for each. The results for 7-day advance bookings are shown in the accompanying table.
a. What confidence coefficient was used to generate the confidence intervals?
b. Give a practical interpretation of each of the 95% confidence intervals. Use the phrase “95% confident” in your answer.
c. When you say you are “95% confident,” what do you mean?
d. If you want to reduce the width of each confidence interval, should you use a smaller or larger confidence coefficient?
Assume that x is a binomial random variable with n = 1000 andp = 0.50. Use a normal approximation to find each of the following probabilities:
a.
b.
c.
Shopping vehicle and judgment. Refer to the Journal ofMarketing Research (December 2011) study of shopping cart design, Exercise 2.85 (p. 112). Recall that design engineers want to know whether the mean choice of the vice-over-virtue score is higher when a consumer’s arm is flexed (as when carrying a shopping basket) than when the consumer’s arm is extended (as when pushing a shopping cart). The average choice score for the n1 = 11 consumers with a flexed arm was = 59, while the average for the n2 = 11
Consumers with an extended arm was = 43. In which scenario is the assumption required for a t-test to compare means more likely to be violated, = 4 and = 2, or, = 10 and = 15? Explain.
Patron amenability to supply biomass. Relate to the Biomass and Energy (Vol. 36, 2012) study of the amenability of directors to supply biomass products similar to fat hay, Exercise8.20 (p. 469). Recall that independent samples of Missouri directors and Illinois directors were surveyed. Another aspect of the study concentrated on the service directors who were willing to supply. One essential service involves windrowing (mowing and piling) hay. Of the 558 Missouri directors surveyed, 187 were willing to offer windrowing. Of the 940 Illinois directors surveyed, 380 were willing to offer windrowing services. The experimenters want to know if the proportion of directors willing to offer windrowing services to the biomass request differs for the two areas, Missouri and Illinois.
a. Specify the parameter of interest to the experimenters.
b. Set up the null and indispensable suppositions for testing whether the proportion of directors willing to offer windrowing services differs in Missouri and Illinois.
c. A Minitab analysis of the data is given below. Detect the test statistic on the printout.
d. provide the rejection region for the test using a = .01.
e. Detect the p- the value of the test on the printout.
f. Make the applicable conclusion using both the p-value and rejection region approach. Your conclusions should agree.
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.)
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