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a. With 90% confidence the proportion of all Americans who favor the new Green initiative is between 0.6290 and 0.6948.
b. If the sample size is changed, the confidence interval changes as the standard error depends on sample size.
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.
Step-by-step explanation:
We have to calculate a 90% confidence interval for the proportion.
The sample proportion is p=0.6619.
The standard error of the proportion is:
The critical z-value for a 90% confidence interval is z=1.6449.
The margin of error (MOE) can be calculated as:
Then, the lower and upper bounds of the confidence interval are:
The 90% confidence interval for the population proportion is (0.6290, 0.6948).