An opinion poll asks a random sample of 100 college seniors how they view their job prospects. In all, 53 say "Good." The 95% confidence interval has a margin of error of 9.9%.
The sample used actually included 130 college seniors but 30 of the seniors refused to answer. This nonreponse could cause the survey result to be in error.
The error due to nonresponse:
A) is included in the margin of error (9.9%) calculated for the confidence interval.
B) is in addition to the margin of error (9.9%) calculated for the confidence interval.
C) can be ignored because it is random.
D) can be ignored because the sample size is greater than 30.
The correct answer is B) is in addition to the margin of error (9.9%) calculated for the confidence interval.
Nonresponse in a survey occurs when some individuals refuse or fail to answer certain questions. In this case, 30 out of the 130 college seniors refused to answer the survey question about their job prospects. The potential error due to nonresponse is separate from the margin of error calculated for the confidence interval.
The margin of error (9.9%) that was calculated for the confidence interval is based on the random sampling variation, assuming no nonresponse. It accounts for the natural variability in the responses of the 100 college seniors who did answer the question.
However, the nonresponse from the 30 college seniors who refused to answer introduces a potential source of bias. It is possible that those who refused to answer may have different job prospects compared to those who answered. This can result in the survey result being in error. In order to account for this potential bias, it is necessary to recognize that the nonresponse itself is an additional source of error in the survey results, separate from the margin of error.
Therefore, the nonresponse error should be considered in addition to the margin of error calculated for the confidence interval.