Supplementary Exercise 6.45 of IPE7e
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Opinion poll on job satisfaction. The focus is on responses in the
category "like job", and 59% out of n=1001 adults gave this response.
The poll reported a maximum margin of error of +- 3%, with 95%
confidence.


(a) We cannot be certain that the true population percent of responses in 
this category falls in the interval 59% +- 3%. Furthermore, there is no
probability associated with whether it falls in the interval, because
the true population percent is a fixed value, and it therefore either is
inside the interval or it is not. The 95% probability is associated with
how we generated the interval, as discussed on slide 5L-12 and explored
in Extra exercise 11. A concrete example of how to compute the
probability that the confidence interval includes the true value is 
shown in Supplementary exercise 5.59 of IPS7e.


(b) We have 95% confidence that the true population percent falls inside
the interval. This means that if we repeated the sampling a large number
of times, in 95% of those repeated samplings the computed interval would
include the true population value. A statement not referring explicitly
to the 95% coverage could be: the researchers would been unlucky with their 
selection of respondents for the interval to not include the true value.


(c) Because the confidence level is 95%, the value zstar used for the 
interval must have been 1.96. Therefore the standard deviation of the
estimate was 0.03/1.96 = 0.015, or 1.5%.


(d) No, the variation included in the confidence interval is purely
random variation from the assumed model. There are many sources of
variation and error not included in that. The estimate can only be
representative for the population it is sampled from, and if the 
sampling method was biased due to undercoverage and nonresponse, the
estimate will not be unbiased for the true population percent (but it
will be unbiased for the population the sampling method actually
covered). The margin of error does also not include variation from a
misspecified model; that is, if some assumptions of the model were not 
met, then the resulting errors will not be included in the margin 
of error.