Mrs. Carrico has been asked to determine the attitude of the students at her school toward a new dress code policy. She asks Paul, a member of the council who is taking AP Statistics, to send a questionnaire to an SRS of 100 students. Eighty-seven students return the completed questionnaire. Paul decides to randomly select 13 additional students to serve as replacement subjects to complete the sample of 100. Is Paul’s sampling method appropriate? Briefly comment on the merits of this method or its pitfalls.

Answer:

Paul's sampling method is not appropriate.

Explanation:

The 13 additional students that Paul selected are not part of the original sample, but make up another sample that should not have been added to the main sample. Only the first 100 students should be considered, in this case, in order not to show sample errors and biased results, Paul should have considered only the 87 students who responded. If an exact response from at least 100 students was so necessary, Paul should have selected a sample larger than 100 students.

Sampling techniques is a fundamental aspect of performing statistical analysis on a subset of the population. The 13 additional students causes a sampling bias, hence Paul's sampling method is inappropriate.

Therefore, the only merit of Paul's action is the increase in sample size which enables the sample to generalize.

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