Question

A sample selected from a population gave a sample proportion equal to 0.61 .

Round your answers to three decimal places.

a. Make a 98 % confidence interval for p assuming n = 75 .

( Enter your answer; confidence interval assuming n=75, lower bound ,Enter your answer; confidence interval assuming n=75, upper bound  )

b. Construct a 98 % confidence interval for p assuming n = 625 .

( Enter your answer; confidence interval assuming n=625, lower bound ,Enter your answer; confidence interval assuming n=625, upper bound  )

c. Make a 98 % confidence interval for p assuming n = 1375 .

( Enter your answer; confidence interval assuming n=1375, lower bound ,Enter your answer; confidence interval assuming n=1375, upper bound  )

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = 0.61

1 - = 1 - 0.61 = 0.39

Z/2 = Z_0.01 = 2.33

a) Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 2.33 (((0.61 * 0.39) / 75)

= 0.131

A 98% confidence interval for population proportion p is ,

± E   

= 0.61  ± 0.131

= ( 0.479, 0.741 )

Lower bound = 0.479, Upper bound = 0.741

b) Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 2.33 (((0.61 * 0.39) / 625)

= 0.045

A 98% confidence interval for population proportion p is ,

± E   

= 0.61  ± 0.045

= ( 0.565, 0.655 )

Lower bound = 0.565, Upper bound = 0.655

c) Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 2.33 (((0.61 * 0.39) / 1375)

= 0.031

A 98% confidence interval for population proportion p is ,

± E   

= 0.61  ± 0.031

= ( 0.579, 0.641 )

Lower bound = 0.579, Upper bound = 0.641