Question
One of the questions on a survey of 1,000 adults asked if today's children will be better off than their parents (Rasmussen Reports website, October 26, 2012). Representative data are shown in the DATAfile named ChildOutlook. A response of Yes indicates that the adult surveyed did think today's children will be better off than their parents. A response of No indicates that the adult surveyed did not think today's children will be better off than their parents. A response of Not Sure was given by 23% of the adults surveyed. The survey results are listed under the question.... perhaps export to excel document.
a. What is the point estimate of the proportion of the population of adults who do think that today's children will be better off than their parents?
b. At 95% confidence, what is the margin of error (to 4 decimals)?
c. What is the 95% confidence interval for the proportion of adults who do think that today's children will be better off than their parents (to 3 decimals)? _______ to _______
d. What is the 95% confidence interval for the proportion of adults who do not think that today's children will be better off than their parents (to 3 decimals)? _______ to _______
e. Which of the confidence intervals in parts (c) and (d) has the smaller margin of error? Part C or D?
Will today's children be better off than their parents? Not sure Not sure Not sure Not sure Yes No No No No No Yes No No Yes No Yes No No No No No No No Yes No Not sure Not sure No Not sure Yes Yes Not sure No No No No No No Not sure No Yes Not sure Yes No Not sure Yes No Yes No No No No Yes No No No Not sure No No Yes No No Yes No No Yes Yes Yes No Not sure Yes Not sure Yes No Yes Yes Not sure No Yes No No No No No No No No No Yes No No No No Yes No No Yes No No No No No Yes Not sure Yes No Not sure No Yes No No Not sure No No No Yes Yes No Not sure No No No No Yes Yes Not sure Not sure Yes Not sure Not sure No Yes No Yes Yes Yes No No Yes No No Not sure Yes No No Not sure No Not sure No No No No No Not sure Not sure Not sure Yes No No No Not sure Yes Not sure No No Not sure Yes No Not sure Yes Not sure Yes Yes Yes No No No Not sure No No Yes No Yes Not sure No Yes Yes Yes Not sure No Not sure No No No Not sure No No No No Not sure Not sure Yes No Yes No No No No No No Yes Not sure No No No No No No No No No Yes Not sure No No Not sure Yes No Yes Yes No No Yes No Not sure No No Not sure No No No Not sure Yes Not sure Not sure No No Yes Not sure Not sure No No Yes No No No Yes No No No Yes No No Yes Not sure Not sure No No No Not sure No No Not sure No No Yes No Not sure Not sure Not sure No Yes Yes No No No No Not sure Yes No Not sure No Yes Yes No Not sure No Not sure No Not sure Yes Yes Not sure No No No No Not sure No No No No Yes No No Yes No No Yes Yes No Not sure Not sure Yes No No No No No No No Yes No No Not sure No Yes No No Not sure No No No No No Not sure Not sure Not sure Not sure Not sure No No No No No No Not sure Yes No Yes No No No Not sure No Not sure Not sure No Yes Yes No Not sure No Yes No No Yes Not sure Yes Yes Yes No Not sure Not sure No No No Not sure No No No No Not sure No Not sure Yes Yes No No No Not sure No No Yes No Not sure Yes No No Not sure Not sure Not sure No Yes No Not sure Yes Yes Not sure Yes Yes Not sure No Not sure Yes Not sure No Not sure Yes No Yes No Yes No No Yes No No No No Yes No No Yes Yes Not sure No Yes Not sure No No No No No No No Yes No Yes Yes No Not sure No Yes Yes Not sure No No No Not sure Yes No Not sure Yes No Not sure No No No No No Yes No Yes No No No No Not sure No Yes Yes Not sure No Yes No No Not sure No Not sure Yes No Not sure Yes Yes No Yes Yes No Yes No No No No No No No No No No Yes Not sure No Not sure No No Not sure No No Not sure No Yes No Yes Yes No No Yes No Not sure No No Yes No No No No No No Not sure Not sure No Yes Not sure No Not sure Not sure No No No Not sure Yes Yes Not sure No No Yes No Not sure No No No Not sure Yes Yes No No No No Not sure Yes No Not sure No No Not sure No No Not sure Yes No No Not sure No No Not sure No No No Yes No No No No Not sure Not sure Yes No Yes No Yes No Not sure Not sure Not sure No Yes Yes No No No No Yes Not sure Not sure Yes No No No No No Yes No Not sure No Yes No No No No Not sure No Yes Not sure Yes No No Not sure Yes No No Not sure No Yes No No Not sure No No Not sure No No Not sure Yes No Yes Not sure No Not sure No Not sure No No Yes No Yes Not sure Yes Yes Not sure No No Not sure No No Not sure Not sure Yes No Not sure No No No No No Not sure No No No No Yes No Not sure Not sure Not sure No No Not sure No Yes No No No No No Yes No Not sure Not sure No Yes Not sure Yes Not sure Not sure No Not sure Yes Not sure Yes No Not sure Yes No No No No Yes Yes No No No Yes No Not sure No Yes Not sure No No Yes No Not sure No No No Yes No Yes No No Not sure Not sure Yes No No Yes No No No No No No No No No Yes No Not sure Yes No No Yes Yes Not sure Yes Yes Not sure Not sure Not sure Yes No Not sure No No Not sure Not sure No No No No No No No Yes No Not sure Yes No Yes No No Not sure Yes No Not sure No No No Not sure Yes No Not sure Not sure Yes No No Not sure Yes Not sure Yes Not sure Yes Yes Yes No Yes Not sure No No No Not sure No Not sure No Not sure Yes Yes Yes No Yes No No No Yes Yes No Not sure Not sure Yes Yes Yes Not sure No No No No No Not sure Not sure No No Not sure No Yes Not sure Not sure No No No No Not sure No No Yes Yes No No Yes No No Yes Not sure Not sure No Not sure Not sure No No No No Yes No No No Not sure Yes Not sure Yes No Not sure Yes Not sure Yes No No No No No Not sure Yes Yes Yes No Not sure Yes No No No Yes No Yes No Yes No Yes Not sure Not sure No No Not sure Yes No No No No No Not sure Yes Yes No Not sure Not sure Yes Yes No Yes No No Not sure No Not sure Not sure Not sure No No No Yes Yes Not sure Yes Yes No Not sure No Not sure Yes No Not sure Yes Not sure Yes Yes No Yes No No Yes No Not sure Yes Not sure No No Not sure No Not sure Not sure No No
Explanation / Answer
a) point estimate =number who saild yes/total surveyed people =x/n =240/1000 =0.24
b) for std error =(p(1-p)/n)1/2 =0.0135
for 95% CI; z =1.96
hence margin of error =z*std error =0.0265
c)
95% confidence interval for the proportion of adults who do think that today's children will be better off than their parents =sample proportion -/+ margin of error =0.214 to 0.266
d)
for people who don't think:
point estimate =530/1000 =0.53
std error =(p(1-p)/n)1/2 =0.0158
for 95% CI; z =1.96
hence margin of error =z*std error =0.0309
95% confidence interval for the proportion of adults who do not think that today's children will be better off than their parents =0.499 to 0.561
e) for part d
