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Chapter 2: Problem 28

The report "Undergraduate Students and Credit Cards in 2004: An Analysis of Usage Rates and Trends" (Nellie Mae, May 2005 ) estimated that \(21 \%\) of undergraduates with credit cards pay them off each month and that the average outstanding balance on undergraduates' credit cards is \(\$ 2169 .\) These estimates were based on an online survey that was sent to 1260 students. Responses were received from 132 of these students. Is it reasonable to generalize the reported estimates to the population of all undergraduate students? Address at least two possible sources of bias in your answer.

Short Answer

Expert verified
No, it is not reasonable to generalize the reported estimates to the whole undergraduate population due to potential biases in the sample selection and response process.

Step by step solution

01

Understanding Bias

Bias in statistics refers to a systematic error that occurs when a sample data set collected does not accurately represent the entire population. The bias in the samples could lead to an inaccurate representation of the population, thus compromising the validity of the findings from the sample.
02

Considering the Sample Size

The sample size in this survey was only 132 out of 1260 students invited to participate. Even though there is no hard rule about what constitutes an acceptable response rate for survey research, this percentage (about \(10.5\% \)) is relatively low, and means the results are not necessarily representative of the entire student population.
03

Considering Selection Bias

The survey was administered online, which likely introduced selection bias. For instance, students without internet access or technological skills, or those who do not regularly check their emails, were probably excluded from potential respondents. As such, the group of students who responded to the survey is likely not representative of the broader population of students.
04

Considering Response Bias

Response bias, a type of bias that influences a subject's response away from an accurate one, may also have played a role here. This could happen if the survey questions were leading or if the students had reasons to lie about their credit card usage, e.g. due to embarrassment or fear of judgement.
05

Conclusion

Considering the sampling methodology and response rate, together with potential biases inherent in the design and administration of the survey, it is not reasonable to generalize the reported estimates to all undergraduate students. There is significant potential for bias in this sample.

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