Question

Suppose we want to study the average number of citations of research papers published by all faculty members. Towards that, we choose 10 departments at random and note down the total number of citations of research papers published by all faculty members in these departments. This is an example of a

	I.	simple random sampling.
	II.	stratified sampling.
	III.	convenience or biased sampling.
	IV.	systematic sampling.
	V.	cluster sampling.

Suppose an urn contains 6 red balls and 5 black balls. Two balls are drawn at random one by one without replacement. Find the probability that exactly one red ball and exactly one black ball will be selected (up to four decimal places).

Hint: Find P(BR or RB).

It has been documented that the placebo effect works on dogs, too. In one study that looked at dogs with arthritis, researchers randomly assigned half of the dogs to receive a placebo pill, and the other half were assigned a pill with active ingredients for treating arthritis. The study was double-blind, in that neither the veterinarian nor the owner (nor the dog) knew which treatment was being used for each of the subjects. What did the researchers do to control for lurking variables?

	I.	(a) They had a control group.
	II.	(b) They used double-blinding.
	III.	(c) They randomly assigned dogs to their treatment groups.
	IV.	(a) and (b)
	V.	(a), (b), and (c)

The five-number summary of credit hours for 24 students in a statistics class is:

Min=6.0

Q1=15.0

Median=16.5

Q3=18.0

Max=22.0

Which statement is true?

	I.	There are both low and high outliers in the data.
	II.	There are no outliers in the data.
	III.	None of the above.
	IV.	There is at least one high outlier in the data.
	V.	There is at least one low outlier in the data.

Determine if the following statement is true or false. Let A and B be two mutually exclusive events with P(A)=0.6 and P(B)=0.75.

n which of the following cases, the use of a Stem and Leaf Plot is not a good choice as a graph?

	I.	A basketball coach who wants to visualize the data of the 15 players on his team.
	II.	An elementary school teacher wants to visualize the data of how her 20 students did on a test.
	III.	A researcher wants to visualize the results of the growth of her 13 plants.
	IV.	A golf player wants to visualize his past 10 scores.
	V.	A professor wants to visualize the data of the scores of her 200 students on a test.

Answer 1

1.

In cluster sampling, we select clusters of sample units and then collect data from all sample units of selected clusters. Here, departments are clusters. We selected 10 departments in random and collected data from all faculty members of these departments.

Hence, this is an example of V. Cluster sampling.

2.

Corresponding probability is given by

Hence, 0.5455 is the probability that exactly one red ball and exactly one black ball will be selected.

3.

From the description, we observe as follows.

• A treatment and a control group were considered.
• Dogs were randomly assigned in a treatment and a control group.
• Neither the veterinarian nor the owner (nor the dog) knew which treatment was being used for each of the subjects i.e. double-blinding was used.

Hence, V. (a), (b) and (c).

4.

Inter-quartile range is given by

Range of non outlier values is given by

We have minimum value 6 outside this range whereas maximum value 22 within this range.

Hence, V. There is at least one low outlier in the data.

5.

Two events A and B are mutually exclusive if

We have,

Thus A and B are not mutually exclusive events.

Hence, the statement is FALSE.

6.

Test scores, golf scores as well as growth are simple numerical value. So, using Stem and Leaf Plot is appropriate in case of II, III, IV and V.

For players in a basketball team, players have records regarding number of scores, number of defends, number of passes, number of fouls and few more. All of these can ot be interpreted using Stem and Leaf Plot efficiently.

Hence, Stem and Leaf Plot is not appropriate in case of I. A basketball coach who wants to visualize the data of the 15 players on his team.