Question 6.49

6.49 Satisfied with your job?

The Gallup-Healthways Well-Being Index is a single metric on a 0 to 100 percentage scale based on six domains of well-being, including life evaluation, emotional health, work environment, physical health, healthy behaviors, and basic access. In 2013, the estimate for the index on the national level is 66.2. Material provided with the results of the poll noted:

Interviews are conducted with respondents on landline telephones and cellular phones, with interviews conducted in Spanish for respondents who are primarily Spanish-speaking.

In 2013, for results based on 178,072 respondents, one can say with 95% confidence that the margin of sampling error for those results is ±0.3 percentage points.15

The poll uses a complex multistage sample design, but the sample percent has approximately a Normal sampling distribution.

  1. The announced poll result was . Can we be certain that the true population percent falls in this interval? Explain your answer.
  2. Explain to someone who knows no statistics what the announced result means.
  3. This confidence interval has the same form we have met earlier:

    What is the standard deviation of the estimated percent?

  4. Does the announced margin of error include errors due to practical problems such as nonresponse? Explain your answer.

6.49

(a) No, we are only 95% confident that the interval covers the true index value for the population. (b) We believe the actual index for the population is in this interval with 95% confidence. (c) 0.153%. (d) No, the interval only accounts for error due to random sampling.