The average cost per square foot for the office rental space in the central
business district is US$23.58 according to a survey. A large real estate
company wants to confirm this figure. The rent of per square foot paid by
95 offices in the central business district were investigated by the company.
Suppose the sample average is US$22.83 per square foot, with a standard
deviation of US$5.11. (25%)
(1) Conduct a hypothesis test using α = 0.05 to determine whether the cost
per square foot reported by the survey should be rejected. (7%)
(2) If the decision in part (1) is to fail to reject and if the actual average cost
per square foot is US$22.30, what is the probability of committing a
Type II error? (10%)
(3) The probability of committing a Type II error is set at 0.2 in part (2).
How large a sample is necessary to meet requirements? (8%)
Imperfections in computer circuit boards and computer chips lend
themselves to statistical treatment. For a particular type of board the
probability of a diode failure is 0.03. Suppose a circuit board contains 200
diodes. (15%)
(1) What is the mean number of failures among the diodes? (3%)
(2) What is the variance? (3%)
(3) The board will work if there is no defective diode. What is the
probability that a board will work? Use (a) binomial distribution, and (b)
Poisson approximate. (9%)
An university bookstore claims that 50% of its customers are satisfied with
the service and prices. (10%)
(1) If this claim is true, what is the probability that in a random sample of
600 customers less than 45% are satisfied? (7%)
(2) Suppose that in a random sample of 600 customers, 270 express
satisfaction with the bookstore. What does this tell you about the
bookstore’s claim? (3%)
Five experts rated three brands of noodles in a taste-testing experiment. A
rating of a 5-point scale (1 = extremely bad, 5 = extremely good) is given for
each of three characteristics: taste, aroma, and hardness of noodles. The
following table displays the summated ratings - accumulated over all three
characteristics. (25%)
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