Question 1

Which of the following best describes a 'population' in statistical studies?

Accepted Answer

The entire group of objects or subjects about which information is required.

Question 2

A company wants to estimate the average satisfaction rating of its customers. They randomly select 500 customers from their email database and receive 200 responses. What is the 'sampling frame' in this scenario?

Accepted Answer

The email database of customers.

Question 3

Which of the following is an example of an experimental study?

Accepted Answer

A randomised control trial (RCT) testing a new drug.

Question 4

Why is random sampling important in statistical studies?

Accepted Answer

It ensures every unit in the sampling frame has an equal chance of being included, reducing bias.

Question 5

In the 1936 Literary Digest poll, what was one major error that led to incorrect predictions?

Accepted Answer

The sample was selected using phone records and club memberships, leading to a biased sample.

Question 6

Which sampling method divides the population into groups and then randomly selects all members from some of these groups?

Accepted Answer

Cluster sampling

Question 7

A manufacturing company samples every 10th item off the production line for quality control. What type of sampling is this?

Accepted Answer

Systematic sampling

Question 8

Which of the following best defines a 'statistic'?

Accepted Answer

A numerical characteristic calculated from the sample.

Question 9

What is the main disadvantage of random sampling?

Accepted Answer

It is difficult to implement in practice.

Question 10

Which of the following is a non-sampling error?

Accepted Answer

Non-response from selected participants.

Question 11

A researcher wants to ensure that all age groups are represented in a survey. She divides the population into age groups and randomly samples from each group. What sampling method is she using?

Accepted Answer

Stratified sampling

Question 12

Which of the following statements about representative samples is TRUE?

Accepted Answer

A representative sample is a mini version of the population with no group omitted or over-represented.

Question 13

Which of the following is an example of a voluntary response sample?

Accepted Answer

A poll where participants call in to express their opinions.

Question 14

Which of the following increases the precision of a sample statistic?

Accepted Answer

Increasing the sample size.

Question 15

A radio station asks listeners to call in and vote for their favorite song. What is the main issue with this sampling method?

Accepted Answer

It is likely to produce a voluntary response bias.

Question 16

Which of the following best describes a 'variable' in statistics?

Accepted Answer

Any quantity we measure whose value varies from one unit to another.

Question 17

A study tracks the cholesterol levels of a group of students over four years. What type of study is this?

Accepted Answer

Longitudinal

Question 18

Which of the following is a key advantage of random sampling?

Accepted Answer

It protects against bias.

Question 19

Suppose a sample statistic is calculated as $$\frac{\sum_{i=1}^{n} x_i}{n}$$, where $$x_i$$ are the observed values and $$n is $$the sample size. What does this formula represent?

Accepted Answer

The sample mean

Question 20

Which of the following scenarios is most likely to result in a biased sample?

Accepted Answer

Using a list of club members to represent all city residents.

Collecting Data: Study Design and Sampling in Statistics

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