The margin of error associated with the confidence interval is 0.02.
The 95% confidence interval for the population proportion is defined as:
p ± z(0.05 / 2) × √[p ( 1 − p )/ n]
We have,
p − z(0.05 / 2) × √[ p ( 1 − p )/ n ] = 0.73 ----------- ( 1 )
p + z(0.05 / 2) × √[ p ( 1 − p )/ n ] = 0.77 ----------- ( 2 )
Adding the above two equations,
p − z(0.05 / 2) × √[ p ( 1 − p )/ n ] + p + z(0.05 / 2) × √[ p ( 1 − p )/ n ] = 0.73 + 0.77
2p = 0.73 + 0.77
2p = 1.5
p = 0.75
Now, Subtracting the equations ( 1 ) and (2),
We get,
p − z(0.05 / 2) × √[ p ( 1 − p )/ n ] - p - z(0.05 / 2) × √[ p ( 1 − p )/ n ] = 0.73 - 0.77
−2 × z(0.05 / 2) × √[ p ( 1 − p )/ n ] = -0.44
z( 0.10 / 2) × √[ p ( 1 − p )/ n] = 0.02
The margin of error is defined by the formula:
M E = z(0.05 / 2) × √[ p ( 1 − p )/ n]
Therefore, The margin of error will be:
M E = 0.02
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