Satisfied with your job? Job satisfaction is one of four workplace measures the Gallup-Healthways Well-Being Index tracks among U.S. workers. The question asked is "Are you satisfied or dissatisfied with your job or the work that you do?" In 2011, 87.5% responded that they were satisfied. Material provided with the results of the poll noted:
Results are based on telephone interviews conducted as part of the Gallup-Healthways Well-Being Index survey Jan. 1--April 30, 2011, with a random sample of 61,889 adults, aged 18 and older, living in all 50 U.S. states and the District of Columbia, selected using random-digit-dial sampling.
For results based on the total sample of national adults, one can say with 95% confidence that the maximum margin of sampling error is 1 percentage point.
The poll uses a complex multistage sample design, but the sample percent has approximately a Normal sampling distribution.
(a) The announced poll result was 87.5% ± 1%. 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 announced result 87.5% ± 1% means.
(c) What is the standard error of the estimated percent?
(d) Does the announced margin of error include errors due to practical problems such as nonresponse? Explain your answer.