Let X and Y be the two numbers appearing on two independent rolls of
a dice. Find (15%, 5% each)
(a) p( |X −Y | ≤ 1)
(b) E(2X )
(c) E(2X+Y )
(a) Use moving averages based on a span of 4 to forecast sales of the 1st
quarter of 2002.
(b) We want to incorporate seasonality factors to account for the pattern
that repeats every four quarters. Calculate the seasonality factor for the
1st quarter.
(c) What is the forecasted sale of the 3rd quarter of 1996 if we used an
exponential smoothing model with a smoothing constant 0.5?
The lifetimes of a component are exponentially distributed with a mean of
10 hours. Find (10%, 5% each)
(a) the probability that a component survives 20 hours.
(b) the probability that the average lifetime of 100 independent components
exceeds 11 hours. (Hint: use normal approximation).
A marketing company conducted a survey for a new product. They have
surveyed 400 males and 400 females. The result showed 240 males and 200
females favored the product. (10%, 5% each)
(a) Construct a 95% confidence interval for the preference difference (in
proportions) between male and female.
(b) If the proportion in the population favoring the product is 50%. What is
the probability of a simple random sample of 625 subjects favoring the
product is between 48% and 52%?
The purchasing director for an industrial parts factory is investigating the
possibility of purchasing a new type of milling machine. She has
determined that the new machine will be bought if there is evidence that
the parts produced have a higher average breaking strength than those
from the old machine. Assume that
μa = average breaking strength for old machine
μb = average breaking strength for new machine
Find the correct statement(s): (10%)
The null hypothesis for this problem is 0 : a b H μ ≥ μ
F test (from ANOVA) can be used to analyze this problem.
Two-Sided Two-Sample T-test can be used to analyze this problem.
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