Question

A newsgroup is interested in constructing a 90% confidence interval for the proportion of all Americans who are in favor of a new Green initiative. Of the 543 randomly selected Americans surveyed, 384 were in favor of the initiative. Round answers to 4 decimal places where possible.

a. With 90% confidence the proportion of all Americans who favor the new Green initiative is between and .

b. If many groups of 543 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

a)

The sample Proportion is

For 90% Confidence Interval, Z_{c} = 1.645

The confidence interval is given by

b)

.About 90 percent of these confidence intervals will contain the true population proportion of Americans who favor the Green initiative and about 10 percent will not contain the true population proportion.

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