Question

Sleepless nights How much sleep do high school students get on a typical school night? An interested student designed a survey to find out. To make data collection easier, the student surveyed the first $100$ students to arrive at school on a particular morning. These students reported an average of $7.2$ hours of sleep on the previous night.

(a) What type of sample did the student obtain?

(b) Explain why this sampling method is biased. Is $7.2$ hours probably higher or lower than the true average amount of sleep last night for all students at the

school? Why?

Short answer

Part (a) The results can be displayed in a convenience sample of the easiest people to approach.

Part (b) Students who did not get enough sleep the night before are more likely to be late the next day.

Step-by-step solution

Part (a) Step 1: Given information

Sample size, $n=100$

Average sleep time, $x=7.2hrs$

Part (a) Step 2: Concept

A simple random sample (SRS) of size n is made up of $n$ people chosen from the population with an equal chance of being the sample that is actually chosen.

Part (a) Step 3: Explanation

Because the student polled the first $100$ kids to arrive at school on a specific morning, it is a convenience sample. Results can be displayed using a convenience sample of individuals who are the easiest to approach.

Part (b) Step 1: Explanation

Because the first $100$ children to arrive at school are indicative of the student population in general, the convenience samples are bound to be biassed. $7.2$ hours is more likely. Students who did not get enough sleep the night before are more likely to be late the next day.