Question

A Gallup poll found that 493 of 1050 adult Americans believe it is the responsibility of the federal government to make sure all Americans have healthcare coverage. Construct and interpret a 90% confidence interval for the proportion of adult americans who believe it is the federal governments responsibility to make sure all americans have coverage? What does this interval suggest?

Answer 1

Sample proportion = 493 / 1050 = 0.470

90% confidence interval for p is

- Z * sqrt ( ( 1 - ) / n) < p < + Z * sqrt ( ( 1 - ) / n)

0.470 - 1.645 *sqrt( 0.470 * 0.530 / 1050) < p < 0.470 + 1.645 *sqrt( 0.470 * 0.530 / 1050)

0.445 < p < 0.495

95% CI is (0.445 , 0.495)

Interpretation -

We are 90% confident that the population proportion of adult Americans who believe it is the federal

governments responsibility to make sure all americans have coverage is between 0.445 and 0.495

Less than 50% of the Americans believe it is the federal governments responsibility to make

sure all Americans have coverage.