6.29 Outlook on life. Since 2008, the Gallup-Healthways Well-Being Index tracks how people feel about their daily lives. In 2014, 54.1% of the respondents were classified as “thriving.” This classification is based on how a respondent rates his or her current and future lives. This is the highest percent of respondents in this category since the index started. Material provided with the results noted:

Results are based on telephone interviews . . . with a random sample of 176,903 adults, living in all 50 U.S. states and the District of Columbia. For results based on the total sample of national adults, the margin of sampling error is ±1 percentage points at the 95% confidence level.¹²

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

1. (a) The announced poll result was 54.1% ± 1%. Can we be certain that the true population percent falls in this interval? Explain your answer.

2. (b) Explain to someone who knows no statistics what the announced result 54.1% ± 1% means.

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   (c) This confidence interval has the same form we have met earlier:

   estimate ± z* σ_estimate

   What is the standard deviation σ_estimate of the estimated percent?

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