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Chapter 4: Problem 9

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?

Short Answer

Expert verified
(a) Convenience sample. (b) The method is biased; 7.2 hours is likely higher than the true average.

Step by step solution

01

Identify the Type of Sample

The sample obtained by the student is a convenience sample. This is because the sample includes only the first 100 students who arrived at school, which is not randomly selected but chosen based on ease of access.
02

Analyze Sampling Bias

Convenience sampling often introduces bias because it does not represent the entire population. In this scenario, students arriving early might have different characteristics (such as better sleep habits or living closer to school) than those arriving later, affecting the representativeness of the sample.
03

Evaluate Whether the Estimate is Likely Higher or Lower

Since early arrivers might be better organized and have time management skills that allow for more sleep, the reported average of 7.2 hours could be higher than the true average amount of sleep for the overall student body, which includes those with less regular sleep patterns or longer commutes.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Convenience Sample
A convenience sample is, as the name suggests, all about convenience. It refers to a sampling method where the researcher selects participants based on ease of access. This means that instead of randomly choosing individuals from the entire population, the sample consists of those who are easy to reach.
This approach is often tempting because it saves time and resources, but it comes with significant drawbacks. In the scenario provided, the student used a convenience sample by surveying the first 100 students who arrived at school. This group was likely chosen because they were readily available at a specific time and location, minimizing the effort needed to gather the data.
Sampling Bias
Sampling bias occurs when the sample collected does not accurately reflect the characteristics of the whole population. This bias can lead to skewed results because the sample is not representative. In the given example, the sampling method introduces bias since only early-arriving students were chosen.
These students might have different attributes compared to those who arrive later, such as living closer or having better time management skills. Such factors can influence their sleep patterns, making their reported average less reflective of the school's entire student population.
  • Not all students were given a chance to be included in the survey.
  • Specific habits or characteristics of early arrivers aren't applicable to all students.
  • The sample's results may not generalize to the broader student body.
Representative Sample
A representative sample is essential for making accurate conclusions about a population. This type of sample mirrors the diversity and characteristics of the entire population, allowing researchers to make valid inferences.
In finding out how much sleep high school students get, a representative sample would include students from various grade levels, academic standings, and personal routines, rather than selectively targeting one specific group.
By using a random sampling method, each student would have an equal opportunity to be included, thus creating a sample that genuinely reflects the student's body. This leads to conclusions that are more likely to hold true for all, not just a particular subset. When creating a representative sample:
  • Use random selection methods.
  • Ensure that diverse characteristics of the population are accounted for.
  • Aim to capture the full scope of variations within the group.

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