Question

You want to determine the proportion of American adult consumers who

spent more money on Christmas gifts in 2015 than they did in 2014. Decide which of the four samples

below is most likely to be a representative sample, and explain why. Then explain why each of the other

three samples is not likely to be representative. [2 points]

a. All customers visiting the South Hills Mall in Pittsburgh between 10am and 2pm on a weekday

b. Every 100th customer visiting the South Hills Mall in Pittsburgh during all the hours it is open for

one whole week

c. All visitors to the website of a TV station in Pittsburgh

d. All attendees of a pro wrestling event at an auditorium in Pittsburgh.

Answer 1

(i)

Correct option:

b. Every 100th customer visiting the South Hills Mall in Pittsburgh during all th hours it is open for one whole week.

EXPLANATION:
Here systematic sampling method is used. The sampling covers throughout the hours it is open. So, it is most likely to be a representative sample.

(ii)

Sample a: Not likely to be a representative.

EXPLANATION:
The sampling covers only 10am and 2 pm on a weekday. it is open. So, it is not likely to be a representative sample.

Sample c: Not likely to be a representative.

EXPLANATION:
The sampling covers only visitors to the website of a TV station in Pittsburgh. So, it is not likely to be a representative sample.

Sample d: Not likely to be a representative.

EXPLANATION:
The sampling covers only attendees of a pro wrestling event at an auditorium in Pittsburgh. So, it is not likely to be a representative sample.