Question

A Gallup poll conducted in November 2010 found that 493 of 1050 adult Americans believe it is the responsibility of the federal government to make sure all Americans have healthcare coverage.

Use Minitab Express to construct the following confidence intervals.  Report your answers as decimals (not percents) rounded to three decimal places, where applicable.

a) We are 95% confident that the proportion of all adult Americans who believe it is the responsibility of the federal government to make sure all Americans have healthcare coverage is between ____ and ____

b) We are 99% confident that the proportion of all adult Americans who believe it is the responsibility of the federal government to make sure all Americans have healthcare coverage is between _____ and ____

Answer 1

a) 95% confidence interval will be :

Upper limit = ( 493 / 1050 ) + Z_0.05/2 * (( 493 / 1050) * ( 1 - ( 493/1050)) / 1050 )^0.5 = 0.499

Lower limit = ( 493 / 1050 ) - Z_0.05/2 * (( 493 / 1050) * ( 1 - ( 493/1050)) / 1050 )^0.5 = 0.439

We are 95% confident that the proportion of all adult Americans who believe it is the responsibility of the federal government to make sure all Americans have healthcare coverage is between 0.439 and 0.499

b)

99% confidence interval will be :

Upper limit = ( 493 / 1050 ) + Z_0.01/2 * (( 493 / 1050) * ( 1 - ( 493/1050)) / 1050 )^0.5 = 0.509

Lower limit = ( 493 / 1050 ) - Z_0.01/2 * (( 493 / 1050) * ( 1 - ( 493/1050)) / 1050 )^0.5 = 0.429

We are 99% confident that the proportion of all adult Americans who believe it is the responsibility of the federal government to make sure all Americans have healthcare coverage is between 0.429 and 0.509