Q 1.70. - Elementary Statistics

Question

University Parking Facilities. During one year, a university wanted to gauge the sentiment of the people using the university's parking facilities. Each of the 8493 people that used the parking facilities had a sticker with a unique number between 1 and 8493. The university committee on parking decided to sample 30 users of the parking facilities and obtain their views on those facilities. The committee selected a number at random between 1 and 283 and got the number 10. The people interviewed were the ones whose stickers had numbers 10, 293, 576, ..., 8217. What type of sampling design was used by the university committee on parking? Explain your answer.

Step-by-Step Solution

Answer

Systematic sampling is used in this study. 

Step 1. Given information.

The given statement is:

During one year, a university wanted to gauge the sentiment of the people using the university's parking facilities. Each of the 8493 people that used the parking facilities had a sticker with a unique number between 1 and 8493. The university committee on parking decided to sample 30 users of the parking facilities and obtain their views on those facilities. The committee selected a number at random between 1 and 283 and got the number 10. The people interviewed were the ones whose stickers had numbers 10, 293, 576, ..., 8217.

Step 2. Explanation.

It is evident from the information provided that a random number 10 is chosen between 1 and 283. 

As a result, the stickers with the numbers 10, 293, 576, and 8217 form the sample of users.

From the above information, it is clear that $k= 10$ and $m= 283 \mathrm{because} \left(293-10\right)=283$

That is, the initial number 10 is fixed, and every 283rd number is chosen, resulting in a sample of these numbers.

As a result, the sampling method employed here is systematic sampling.