In an August 2012 Gallup survery of ,1012 randomly selected U.S. adults, 53% said that they were dissatisfied with the quality of education students receive in kindergarten through grade 12.
a) Verify that the sample is large enough to use the normal formula to find a confidence interval for the proportion of Americans who are dissatisfied with the qualit of education students receive in kindergarten through grade 12.
b) Construct a 90% confidence interval for the proportion of U. S. adults who are dissatisfied with the quality of education students receive in kindergarten through grade 12. Use three decimal places i your margin of error.
c) Suppose you want to estimate the proportion of local adults who are dissatisfied with the education students receive in kindergarten through grade 12 with 95% confidence and a 55 margin of error. If you suspect that local adults won't differ drastically from those Gallup used, how many people should you sample?
d) Test, at the 5% level, if this sample provides evidence that the proportion of Americans who are dissatisfied with education in kindergarten through grade 12 differs significantly from 50% . Be sure to verify that it is appropriate to use a normal distribution to compute the p-value and include all of the details of the test.