Final answer:
The random variables X and P' are defined in words. The binomial distribution should be used for this problem. A 95 percent confidence interval is constructed for the population proportion of American adults who are worried a lot about the quality of education in our schools.
Step-by-step explanation:
Define the random variables X and P' in words.
X: The number of adults who believe that the overall state of moral values is poor.
P': The population proportion of adult Americans who are worried a lot about the quality of education in our schools.
Which distribution should you use for this problem? Explain your choice.
For the problem of finding the population proportion, we should use the binomial distribution. The binomial distribution is appropriate when there are two possible outcomes (in this case, worried a lot or not worried a lot) and when the trials are independent.
Construct a 95 percent confidence interval for the population proportion of adult Americans who are worried a lot about the quality of education in our schools.
i. The confidence interval is (0.598, 0.662)
ii. The graph of the confidence interval would show a range of proportion values centered around the point estimate.
iii. The error bound is equal to half the width of the confidence interval, which is (0.662-0.598)/2 = 0.032.