Question

A newsgroup is interested in constructing a 99% confidence interval for the proportion of all Americans who are in favor of a new Green initiative. Of the 534 randomly selected Americans surveyed, 400 were in favor of the initiative.

a. With 99% confidence the proportion of all Americans who favor the new Green initiative is between -- and --.

b. If many groups of 534 randomly selected Americans were surveyed, then a different confidence interval would be produced from each group. About -- . percent of these confidence intervals will contain the true population proportion of Americans who favor the Green initiative and about -- percent will not contain the true population proportion.​

Answer 1

Solution: a. With 99% confidence the proportion of all Americans who favor the new Green initiative is between -- and --.

Answer: We are given:

Number of people who are in favor of the intiative,

Therefore the sample proportion is given below:

Now the 99% confidence interval is given below:

is the critical value at 0.01 significance level and is given:

rounded to two decimal places.

Therefore, with 99% confidence the proportion of all Americans who favor the new Green initiative is between 0.70 and 0.80.

b. If many groups of 534 randomly selected Americans were surveyed, then a different confidence interval would be produced from each group. About -- . percent of these confidence intervals will contain the true population proportion of Americans who favor the Green initiative and about -- percent will not contain the true population proportion.​

Answer: If many groups of 534 randomly selected Americans were surveyed, then a different confidence interval would be produced from each group. About 99 percent of these confidence intervals will contain the true population proportion of Americans who favor the Green initiative and about 1 percent will not contain the true population proportion.​