99年國立交通大學科技管理研究所統計學線上測驗

1.
(A): Events A and B are dependent.
(B): Events A and B are independent.
(C): Events A and B are mutually exclusive.
(D): Events A and B have no sample points in common.

2.

A sample of 200 shoppers at a large department store X were asked two questions:
(1) Did you see a television ad for the sale at department store X during the past 2
weeks?
(2) Did you shop at department store X during the past 2 weeks? The responses to
the questions are summarized in the table.

What is the probability that a randomly chosen shopper did not see the ad and did not
shop at department store X ?

(A)

0.6

(B)

0.05

(C)

0.1

(D)

0.25

3.: A human gene carries a certain disease from a mother to her child with a probability
rate of 0.40. That is, there is a 40% chance that the child becomes infected with the
disease. Suppose a female carrier of the gene was three children. Assume that the
infections, or lack thereof, are independent of one another. Find the probability that
none of the children get the disease from their mother.
(A): 0.064
(B): 0.096
(C): 0.216
(D): 0.4

4.: A 99% confidence interval for the average salary of all CEOs in the electronics
industry was constructed sing the results of a random survey of 45 CEOs. The interval
was (NT$2,885,363, NT$3,120,019). To make more useful inferences from the data, it
is desired to reduce the width of the confidence interval. Which of the following will
result in a reduced interval width?
(A): Increase the sample size and increase the confidence level.
(B): Decrease the sample size and decrease the confidence level.
(C): Increase the sample size and decrease the confidence level.
(D): Decrease the sample size and increase the confidence level.

5.: A 99% confidence interval for the average salary of all CEOs in the electronics
industry was constructed sing the results of a random survey of 45 CEOs. The interval
was (NT$2,885,363, NT$3,120,019). Give practical interpretation of the interval.
(A): We are 99% confident that the mean salary of the sampled CEOs falls in the
interval NT$2,885,363 to NT$3,120,019.
(B): We are 99% confident that the mean salary of all CEOs in the electronics industry
falls in the interval (NT$2,885,363, NT$3,120,019)
(C): 99% of all CEOs in the electronics industry have salaries that fall between
NT$2,885,363 to NT$3,120,019.
(D): 99% of the sampled CEOs have salaries that fell in the interval NT$2,885,363 to
NT$3,120,019.

6.: A significance level for a hypothesis test is given as α = .05 . Interpret this value.
(A): There is a 5% chance that the sample will be biased.
(B): The smallest value of α that you can use and still reject 0 H is .05.
(C): The probability of making a Type II error is .95.
(D): The probability of making a Type I error is .05.

7.: We sampled 100 men and 100 women and asked: “Do you think the environment is a
major concern in 2010?” Of those sampled, 67 women and 63 men responded that they
believed it is. For the confidence interval procedure to work properly, what additional
assumptions must be satisfied?
(A): Both samples were randomly and independently selected from their respective populations.
(B): The population variances are equal.
(C): Both populations have approximate normal distributions.
(D): All of the above are necessary.

8.: Which of the following is NOT a condition required for a valid ANOVA F-test for a
completely randomized experiment?
(A): The variances of all the sampled populations are equal.
(B): The samples are chosen from each population in an independent manner.
(C): The sampled populations all have distributions that are approximately normal.
(D): The sample chosen from each of the populations is sufficiently large.

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