These data should not be used to construct a confidence interval for the mean score of all the students in the college because the sample of students is not representative of the population of all students in the college. Here are the reasons:

1. Sample Bias: The sample consists only of the students in one psychology professor's class. These students may not represent the broader student body due to factors such as differences in academic programs, interests, or exposure to the professor's teaching style.

2. Population Scope: The test scores are only from a specific subset (the professor's class) rather than a random or diverse sample from the entire student population. For a confidence interval to be valid, the sample should ideally be randomly selected to ensure that it reflects the characteristics of the whole population.

3. Potential Influence of Context: The professor's own teaching methods or the class environment may have influenced the students' attitudes, leading to scores that do not generalize beyond that class.

4. Sample Size Limitation: While the sample size of 30 is sufficient for constructing a confidence interval under normal distribution assumptions, the lack of randomness in the sample selection undermines its validity for population-level inferences.

5. Representation of Variability: The attitudes of students across the college may have a different mean or standard deviation than those in the psychology professor's class. Without a proper sampling method, we cannot account for this variability.

Conclusion:

To construct a valid confidence interval for the mean score of all college students, the data must come from a sample that is randomly selected and representative of the entire population. Since this criterion is not met, these data are unsuitable for this purpose.

Would you like to dive deeper into sampling methods or the implications of sample bias?

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Related Questions:

1. What is the importance of random sampling in statistical inference?
2. How does sample size affect the reliability of a confidence interval?
3. Can data from a biased sample ever be adjusted to approximate population parameters?
4. What statistical tests can verify if a sample represents a population?
5. Why is normality important in constructing confidence intervals?

Tip:

Always assess whether your sample is random and representative before making population-level inferences using statistical methods.