Sampling and proportions — Question 191

Original QCE Vault practice · 1 mark

Q191 · Practice questionTechnology-freeSimple familiar1 mark

QUESTION 191

Which method is most likely to give a random sample of customers from a database of

5000

customers?

(A)

Select the first 100 customers alphabetically.

(B)

Ask for 100 volunteers through a social-media post.

(C)

Assign each customer a number and use a random-number generator to select 100 distinct numbers.

(D)

Survey the next 100 customers who make a purchase.

ABCD

Question linkSyllabus coverage

WORKED SOLUTION

Answer C

1 mark

ANSWER

Worked solution

Randomly selecting IDs from the full sampling frame gives each customer a random chance of selection and avoids obvious convenience or voluntary-response bias.

Selects the correct option.

[1 mark]

Practice question aligned to the current QCAA syllabus; review the worked solution and marking criteria.

View the QCAA syllabus

Related questions

Q9 · Original practice · 1 mark
In a random sample of 200 voters, 54 support a proposal. The sample proportion is
Sampling and proportions
Q19 · Original practice · 1 mark
For repeated samples of size 400 from a population with proportion $p=0.30$ , the standard deviation of $\hat p$ is closest to
Sampling and proportions
Q34 · Original practice · 3 marks
A population has proportion $p=0.60$ . For random samples of size 250, determine the mean and standard deviation of the sampling distribution of $\hat p$ .
Sampling and proportions
Q44 · Original practice · 5 marks
A manufacturer claims that the proportion of defective components is $p=0.08$ . In a random sample of 300 components, 34 are defective. Assuming the claim is correct, use a normal approximation to determine the probability of obtaining a sample proportion at least as large as the observed value. Comment on whether the result would be unusual at the 5% level.
Sampling and proportions