The Taipei City government showed that a family spends an average of
NT$1,526.9 per month traveling. Suppose a sample of 64 families traveling
during February’s Taiwanese New Year vacation resulted in a sample
mean of NT$1,566.20 and a sample standard deviation of NT$87.64. A 95%
confidence interval estimate of the mean amount spent per month by a
family during February’s Taiwanese New Year vacation is ________. (4%)
The Council of Labor Affairs, Executive Yuan, Taiwan, reported the
average monthly salary for trade and retail industry employees in Taiwan
is NT$56,953. Assume the population mean is μ = NT$56,953 and the
population standard deviation is σ = NT$16,104. Suppose a random
sample of 50 trade and retail industry employees will be selected from the
population. The value of the standard error of the mean is ________. The
probability that the sample mean will be within NT$3,200 of the
population mean is ________. (each 3%)
The population mean monthly salary for public school teacher in Taiwan is
NT$48,973. A sample of the mean monthly salary of public school teachers
in Taipei City is NT$50,867. Assume the Taipei City mean figure is based
on a sample of 95 teachers. Assume the population standard deviation is
σ = NT$6,818. The null hypothesis that can be used to determine whether
the sample data support the conclusion that public school teachers in
Taipei City have a higher mean salary than the rest of public school
teachers in Taiwan is ________. The p-value is ________. (each 3%)
Peggy knows that a certain letter is equally likely to be in any one of three
different folders. Let pi be the probability that Peggy will find her letter
upon making a quick examination of folder i if the letter is, in fact, in
folder i , i = 1, 2, 3 . ( pi < 1 ). Suppose she looks in folder 1 and does not
find the letter. The probability that the letter is in folder 1 is ________.
(6%)
Suppose that each coupon obtained is, independent of what has been
previously obtained, equally likely to be any of m different types. The
expected number of coupons one needs to obtain in order to have at least
one of each type is ________. (6%)
Let X be an exponential random variable with mean 1/λ .
E[X |X > 1] = ________. (6%)
Consider a gambler who at each play of the game has probability p of
winning one unit and probability 1 − p of losing one unit. Assume that
successive plays of the game are independent. The probability that,
starting with i units, the gambler’s fortune will reach N before
reaching 0 is ________. (8%)
The CCU post office is run by two clerks. Suppose that when Professor
Chen enters the system he discovers that Professor Kao is being served by
one of the clerks and Professor Ay by the other. Suppose also that
Professor Chen is told that his service will begin as soon as either Kao or
Ay leaves. The amount of time that clerk i spends with a customer is
exponential distributed with mean 1/λ2 , i = 1, 2. The probability that, of
the three customers, Professor Chen is not the last to leave the post office
is ________. (8%)
Demonstrate how to use the multiple regression approach to test if
there is a significant difference in the means of the three populations in
problem 9. [Hint: You can use the dummy variables to represent the
observations associated with the three populations] (10%)
(i) Give a formula to calculate the multiple coefficient of determination
(R2 ) for a muiltiple regression equation. (5%)
(ii) Give a formula to describe the relationship between adjusted R2 and
R2 . Which one do you prefer to use for model selection? Justify your
answer. (5%)
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