Question

Is your food safe? (8.1) “Do you feel confident or not confident that the food available at most grocery stores is safe to eat?” When a Gallup poll asked this question, $87\%$ of the sample said they were confident.19 Gallup announced the poll’s margin of error for $95\%$ confidence as $\pm 3$ percentage points. Which of the following sources of error are included in this margin of error? Explain your answer.

a. Gallup dialed landline telephone numbers at random and so missed all people without landline phones, including people whose only phone is a cell phone.

b. Some people whose numbers were chosen never answered the phone in several calls or answered but refused to participate in the poll.

c. There is chance variation in the random selection of telephone numbers.

Short answer

Part (a) Not included.

Part (b) Not included.

Part (c) Included.

Step-by-step solution

Part (a) Step 1: Given information

The margin of error for $95$ percent confidence in the poll was $\pm 3$ percentage points, according to Gallup.

Part (a) Step 2: Explanation

Only sampling error is included in the margin of error:

In addition to sampling errors, there are three types of errors that are not mentioned.

• Selection bias can exclude a segment of the population
• Response bias measurement can employ a technique that yields a value that differs significantly from the true value
• Non-response bias occurs when there isn't enough information for everyone in the sample.

Because not everyone has a chance to be included in the sample, the error is choice bias, which, as we all know, is not contained within the margin of error.

Part (b) Step 1: Explanation

Only sampling error is included in the margin of error:

There are three types of errors that sampling error does not cover.

• Selection bias will cause a portion of the population to be excluded.
• Measurement or response bias can use a technique that produces a value that is completely different from the true value.
• Non-response bias occurs when there isn't enough information for everyone in the sample.

Because not everyone in the sample responded, the error is non-response bias, which we all know is beyond the margin of error.

Part (c) Step 1: Explanation

Only sampling error is included in the margin of error:

There are three types of errors that sampling error does not cover.

• Selection bias can exclude a portion of the population
• Measurement of response bias can employ a technique that yields a value that differs significantly from the truth value
• Non-response bias occurs when there isn't enough information for everyone in the sample.

The error is attributed to chance, which is lower than sampling error, therefore it is contained within the margin of error.