Question

Are you feeling stressed? (4.1) A Gallup Poll asked whether people experienced stress “a lot of the day yesterday.” Forty percent said they did. Gallup’s report said, “Results are based on telephone interviews with $178,545$ national adults,

aged $18$ and older, conducted Jan. $2–June30,2009.”4$

(a) Identify the population and the sample.

(b) Explain how undercover could lead to bias in this survey.

Short answer

Part (a) is a sample of $178545$ adults from around the country.

Part (b) results in a bias in coverage.

Step-by-step solution

Part (a) Step 1. Given Information 

Percentage of respondents who indicated they were stressed for much of the day yesterday $=41\%$ Number of adults aged $18$ and up: $353564$

Part (a) Step 2. Concept Used  

We can't foresee the outcomes of a chance process, yet they have a regular distribution over a large number of repetitions. According to the law of large numbers, the fraction of times a specific event occurs in numerous repetitions approaches a single number. The likelihood of a chance outcome is its long-run relative frequency. A probability is a number between $0$(never happens) and $1$(happens frequently) (always occurs).

Part (a) Step 3. Explanation   

In a Gallup poll, participants were asked if they had been stressed "for most of the day yesterday." They did, according to $40\%$ of those polled. "Results are based on telephone interviews $178545$ with national people, aged 18 and older," according to Gallup's study. To begin, you must first comprehend the concepts of sample and population. The population is the total number of people who could have the trait of interest in a study. The sample is the subset of the population on which the actual study is conducted and the relevant measurements are taken. The population is made up of adults from all around the country. The telephone interviews were conducted with $178545$ adults from across the country.

Part (b) Step 1. Explanation   

In a Gallup poll, participants were asked if they had been stressed "for most of the day yesterday." They did, according to $40\%$ of those polled. "Results are based on telephone interviews with $178545$ national people, aged 18 and older," according to Gallup's report. The survey is conducted over the phone. As a result, persons who do not have access to a telephone may have a different viewpoint. As a result, the chosen sample is not representative of the population. As a result, there is a coverage bias.