Question

2) A market research company wishes to find out which of two internet search engines the
population of students at a university prefers to use: Google or MSN Search. A random sample
of students is selected, and each one is asked to search for a certain subject using Google and
then MSN, or vice versa. The order of the two searches was determined at random. They then
indicate which internet search engine they prefer. What type of study is this?

A) An observational study. B) Completely randomized design.
C) A double-blind experiment. D) A matched-pairs experiment.

3) Suppose that A and B are two independent events with P(A) = 0.3 and P(B) = 0.3. Let
Bc be the complement of B. What is P(A and Bc)?
A) 0.09

B) 0.21

C) 0.49

D) 0.60.

4) Which of the following is NOT an assumption of the Binomial distribution?
A) All trials must be independent.
B) Each trial must be classified as a success or a failure.
C) The number of successes in the trials is counted.
D) The probability of success is equal to .5 in all trials.

5) In hypothesis testing, the term “significant difference” refers to
A) the difference between the critical value and the test statistic.
B) the difference between the sample standard deviation and the population mean.
C) the difference between the sample mean and the hypothetical population mean that leads
to the rejection of the null hypothesis.
D) none of the above.

6) The AMS wants to survey students’ opinions about the food services offered in the Student
Union Building. They take a simple random sample of 30 students from each faculty (Arts,
Science, Forestry, . . ., etc.). That is, they get 30 respondents from every faculty. What kind of
survey is this?
A) A probability sample. B) A stratified sample.
C) A simple random sample. D) None of the above.

7) Ignoring twins and other multiple births, assume babies born at a hospital are independent
events, with the probability that a baby is a boy and the probability that a baby is a girl both
equal to 0.5. Define the following events: event A = the next two babies are boys and event
B = the next two babies are girls. These two events are
A) disjoint. B) complements of each other. C) independent. D) both A) and B).

8) Suppose that a particular candidate for public office is in fact favored by p = 48% of all
registered voters. A polling organization is about to take a simple random sample of votes
and will use ˆp, the sample proportion, to estimate p. How many votes need to be sampled to
guarantee that the standard deviation σpˆ is no more than 0.025?
A) 249 B) 399 C) 250 D) 400

9) In a hypothesis testing problem, the P-value tells us
A) if the null hypothesis is true.
B) if the alternative hypothesis is true.
C) the evidence against the null hypothesis.
D) the evidence against the alternative hypothesis.

10) The weight of a randomly selected book is a random variable with a mean of 1 kg and a
standard deviation of 0.5 kg. If we independently pick two books at random, the difference in
the weights of the two books is a random variable with a standard deviation (in kg) of
A) 0.00 B) 1.00 C) 1.41 D) 2.00 E) 0.707.

Answer 1

(2): In the matched pairs experiment, the number of subjects remains same in both the samples.

In the given study, the researcher wants to find out of the most search engines (Google or MSN search) by the population of students at a university. From the university, random sample of students is selected and each one is asked to search for a certain subject using Google and then MSN, or vice versa. Here, there are two treatments-one is Google and the other is MSN. The number of subjects used in both the treatments are same, so it is the case of matched pairs experiment.

Hence, the correct option is D).

(3): It is given that P(A) = 0.3 and P(B) = 0.3.

P(Bc) = 1 – P(B) = 1 – 0.3 = 0.7

Since, the events A and B are independent, so

P(A and Bc) = P(A) * P(Bc) = 0.3 * 0.7 = 0.21

Therefore, the correct option is B).