Question

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 sanple 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?

Name: Problem 9, Chapter 4: The Practice of Statistics for AP
Uploaded: 2022-03-21T20:05:21-08:00
Duration: 1 min 20 s
Channel: Emily Himsel

   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 sanple 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?

The Practice of Statistics for AP

Daren S. Starnes,… 5th Edition

Chapter 4, Problem 9

Instant Answer

Solved by Expert Emily Himsel

03/21/2022

Step 1

This is known as a convenience sample because the student chose the easiest group of people to reach, in this case, the first 100 students to arrive at school. So, the answer to part (a) is a convenience sample. In LaTeX format: The student obtained a Show more…

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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 sanple 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?

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Key Concepts

Convenience Sampling

Convenience sampling is a non-random sampling method where the sample is taken from a group that is easy to access or contact. In the context of this study, selecting the first 100 students to arrive at school means the sample was chosen out of convenience rather than by random selection, which means it may not truly represent the entire population of high school students.

Sampling Bias

Sampling bias occurs when certain members of a population are more likely to be included in the sample than others, leading to a non-representative sample. In this case, because the survey only included early arriving students, it likely favors individuals who may have different sleep patterns (for example, waking up earlier and potentially sleeping less) compared to those who arrive later, making the estimated average of 7.2 hours biased with respect to the true average for all students.

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