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Jerry tested 30 laptop computers owned by classmates enrolled in a large computer science class and discovered that 22 were infected with keystroke- tracking spyware. Is it appropriate for Jerry to use his data to estimate the proportion of all laptops infected with such spyware? Explain.

Short Answer

Expert verified
No, Jerry's data is not appropriate for such generalization due to sample bias and size.

Step by step solution

01

Understanding the Sample

Jerry collected data from 30 laptops owned by classmates enrolled in a specific computer science class. This means his sample is composed of students who are likely to have a common academic background and access to similar resources.
02

Recognizing Sample Bias

The sample may not be representative of the entire population of laptops, as the laptops were all from a particular group: classmates in a computer science class. They may have similar exposure to risks or habits compared to the general laptop user population.
03

Evaluating Sample Size

The sample size of 30 is relatively small when considering the vast number of laptops globally or even within a single country. Small samples can lead to higher margins of error in estimating the actual proportion.
04

Statistical Generalization

The ability to generalize findings from a sample to a larger population depends on how representative and random the sample is. Jerry's sample does not appear to be randomly selected from all laptops worldwide, creating a limitation on the generalization.

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Key Concepts

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

Sample Bias
Sample bias occurs when the sample used in an analysis is not representative of the overall population. In Jerry's case, the sample was biased because all the laptops came from classmates in a specific computer science class. These students likely share similar tendencies, such as using similar networks, websites, and installed software.
This increases their chances of having exposure to the same type of threats, like keystroke-tracking spyware. This type of sample can result in skewed findings because it does not accurately reflect the diversity or characteristics of the wider population.
Understanding sample bias is crucial when collecting data because it influences the reliability of conclusions or predictions. A biased sample might suggest trends or patterns that aren't present in the larger picture, leading to misleading results. To combat sample bias, ensure your selection process aims to represent the entire intended population as accurately as possible.
Sample Size
The concept of sample size refers to the number of observations or data points included in a sample for study. Jerry's sample consisted of 30 laptops, which is considered small, especially given the large number of laptops worldwide.
A smaller sample size can affect the reliability of the findings as it may not capture the diversity and variability necessary for a statistically powerful result. Particularly, small samples are more prone to random error, resulting in less precise estimates of a population's characteristics.
In statistical studies, larger samples generally provide more accurate estimates as they tend to average out anomalies and present a clearer picture. When determining sample size, consider the scope and scale of the study to ensure it is sufficient to draw reliable conclusions from the findings. This means, for a more generalized conclusion about spyware on laptops, Jerry would need a larger and more varied sample.
Generalization
Generalization involves extending findings from the sample group to a larger population. For Jerry's study of 30 laptops, achieving true generalization is challenging because the sample was not random or representative of all laptop users.
To generalize results effectively, the sample must reflect the population's diversity and be collected using random sampling methods, where each member of the population has an equal chance of being chosen.
When a sample is not representative, any conclusions drawn might only be applicable to the sample itself and not to a broader audience. In Jerry's case, the sample of his classmates fails to account for variability in laptop usage, demographics, and external factors that could influence spyware exposure in the larger population.
Proper generalization enables better policy decisions, marketing strategies, and science-based conclusions, making it a fundamental step in the research process. Aim for representativeness and randomness to allow broader application of study results.

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Most popular questions from this chapter

Josh and Kendra each calculated a \(90 \%\) confidence interval for the difference of means using a Student's \(t\) distribution for random samples of size \(n_{1}=20\) and \(n_{2}=31\). Kendra followed the convention of using the smaller sample size to compute d.f. \(=19 .\) Josh used his calculator and Satterthwaite's approximation and obtained \(d . f . \approx 36.3 .\) Which confidence interval is shorter? Which confidence interval is more conservative in the sense that the margin of error is larger?

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