Question

Suppose a polling agency reported that 48.0​% of registered voters were in favor of raising income taxes to pay down the national debt. The agency states that results are based on telephone interviews with a random sample of 1033 registered voters. Suppose the agency states the margin of error for 95​% confidence is 3.0​%. Determine and interpret the confidence interval for the proportion of registered voters who are in favor of raising income taxes to pay down the national debt. ▼ We are 48.0% confident There is a 95% probability We are 95% confident There is a 3.0% probability We are 1033% confident We are 3.0% confident There is a 48.0% probability There is a 1033% probability that the proportion of ▼ all Americans registered voters adult Americans aged 18 or older in favor of raising income taxes to pay down the national debt is between nothing and nothing

Answer 1

The 95% confidence interval for the proportion of registered voters who are in favor of raising income taxes to pay down the national debt is (45%, 51%). This means that we are 95% sure that the true proportion of all registered voters who are in favor of raising income taxes to pay down the national debt is between these two values, of 45% and 51%.

Explanation:

A confidence interval is the sample proportion plus/minus the margin of error.

x% confidence interval:

A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.

In this question:

Sample proportion of 48%.

Suppose the agency states the margin of error for 95​% confidence is 3.0​%. Determine and interpret the confidence interval for the proportion of registered voters who are in favor of raising income taxes to pay down the national debt.

48% - 3% = 45%

48% + 3% = 51%

The 95% confidence interval for the proportion of registered voters who are in favor of raising income taxes to pay down the national debt is (45%, 51%). This means that we are 95% sure that the true proportion of all registered voters who are in favor of raising income taxes to pay down the national debt is between these two values, of 45% and 51%.