What Margin of Error Doesn't Account for?

The principal of a large high school wanted to know how many hours students spend doing homework during a typical week. After randomly selecting the 100 students, the principal personally interviewed the students about their homework habits, including how many hours they spend doing homework in a typical week. Based on the random sample of 100 students, a 90% confidence interval for the mean number of hours doing homework for all students is 2.3 to 4.1 hours. Describe one potential source of bias in the study that is not accounted for by the margin of error.

• Many students may lie about their homework habits when having to respond to the principal without anonymity. The mean number of hours spent on homework for all students may be even less than 2.3 hours.

• Many students would not lie about their homework habits when having to respond to the principal without anonymity. The mean number of hours spent on homework for all students may be even be 2.3 hours.

• Many students may lie about their homework habits when having to respond to the principal without anonymity. The mean number of hours spent on homework for all students may be more than 2.3 hours.

• Many students would not lie about their homework habits when having to respond to the principal without anonymity. The mean number of hours spent on homework for all students may be more than 2.3 hours.

The puzzle editor of a game magazine asked 43 randomly selected subscribers how long it took them to complete a certain crossword puzzle. The 99% confidence interval for the median completion time for all subscribers is 15.2 to 18.6 minutes. The puzzle editor originally sent requests for completion times to 150 subscribers, only 43 of whom reported their times. Describe one potential source of bias in the study that is not accounted for by the margin of error.

• People embarrassed by their puzzle completion time may be less likely to respond (nonresponse). The mean puzzle completion time for all subscribers may be even more than 18.6 minutes.

• People embarrassed by their puzzle completion time may be less likely to respond (nonresponse). The mean puzzle completion time for all subscribers may be less than 18.6 minutes.

• People embarrassed by their puzzle completion time may be more likely to respond (nonresponse). The mean puzzle completion time for all subscribers may be even more than 18.6 minutes.

• People embarrassed by their puzzle completion time may be more likely to respond (nonresponse). The mean puzzle completion time for all subscribers may be even less than 18.6 minutes.

A New York Times/CBS News poll asked a random sample of U.S. adults, "Do you favor an amendment to the Constitution that would permit organized prayer in public schools?" Based on this poll, the 95% confidence interval for the proportion of all U.S. adults who favor such an amendment is 0.63 to 0.69. The news article goes on to say: "The theoretical errors do not take into account additional error resulting from various practical difficulties in taking any survey of public opinion." List some of the "practical difficulties" that may cause errors not included in the ±3 percentage point margin of error.

• Those people selected for the sample may not be available to respond or may refuse to answer (nonresponse). Also, people may answer "Yes" because they think they should, even if they don't support the amendment (response bias).

• Those people selected for the sample may not be available to respond or may refuse to answer (response bias). Also, people may answer "Yes" because they think they should, even if they don't support the amendment (nonresponse bias).

• Those people selected for the sample may be available to respond or may refuse to answer (nonresponse). Also, people may answer "Yes" because they think they should, even if they do support the amendment (response bias).

• Those people selected for the sample may be available to respond or may refuse to answer (response). Also, people may answer "Yes" because they think they should, even if they do support the amendment (nonresponse bias).

A Gallup poll asked a random sample of U.S. adults, "Would you like to lose weight?" Based on this poll, the 95% confidence interval for the proportion of all U.S. adults who want to lose weight is 0.56 to 0.62. Gallup states that the 3 percentage point margin of error for this poll includes only sampling variability (what it calls "sampling error.") What other potential sources of error (Gallup calls these "nonsampling errors") could affect the accuracy of the 95% confidence interval?

• Those people selected for the sample may not be available to respond or may refuse to answer (nonresponse). Also, people may answer "Yes" because they know that they should lose weight, even if they don't want to (response bias).

• Those people selected for the sample may not be available to respond or may refuse to answer (response). Also, people may answer "Yes" because they know that they should lose weight, even if they don't want to (nonresponse bias).

• Those people selected for the sample may be available to respond or may refuse to answer (nonresponse). Also, people may answer "No" because they know that they should lose weight, even if they don't want to (response bias).

• Those people selected for the sample may be available to respond or may refuse to answer (response). Also, people may answer "No" because they know that they should lose weight, even if they don't want to (nonresponse bias).