In 2103 a poll estimated the Well-Being index based on six domains of well-being
ID: 3359041 • Letter: I
Question
In 2103 a poll estimated the Well-Being index based on six domains of well-being, including life evaluation, emotional health, work environment, physical health, healthy behaviors, and basic access. The estimate was 66.2% on the national level. The following statement is from the poll:
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. a. The announced poll result was 66.2 ± 0.3%.
a. Can we be certain that the true population percent falls in this interval? Explain your answer.
b. Explain to someone who knows no statistics what the announce result 66.2 ± 0.3% means.
c. This confidence interval has the same form we have met earlier; estimate ± z*estimate. What is the standard deviation estimate of the estimated percent?
please show step by step
Explanation / Answer
Ans:
The given estimate at national level=66.2%
And number of observations (n)=178072
And 95% confidence interval of true population percent
=66.2+_0.3%
(A)yes we 95 % confident that our calculated percentage will fall in this interval with given margin
(B) then this 95% confidence interval means if we take samples 100 times then 95 times calculated percentage of national fall in this interval
(C)note that
Estimate +_margin error=66.2%+_.03%
So (Sigma)*z(alpha)/n=.0003
So Sigma=(178072*.0003)÷(z alpha)
Sigma=(421.98*.0003)÷1.96
Sigma=.0642