Question

Credit card ownership varies across age groups. Suppose that the estimated percentage of people who own at least one credit card is 64% in the 18–24 age group, 84% in the 25–34 age group, 77% in the 35–49 age group, and 79% in the 50+ age group. Suppose these estimates are based on 465 randomly selected people from each age group.

(a) Construct a 95% confidence interval for the proportion of people in the 18–24 age group who own at least one credit card. (Round your answers to four decimal places.)

Construct a 95% confidence interval for the proportion of people in the 25–34 age group who own at least one credit card. (Round your answers to four decimal places.)

Construct a 95% confidence interval for the proportion of people in the 35–49 age group who own at least one credit card. (Round your answers to four decimal places.)

Construct a 95% confidence interval for the proportion of people in the 50+ age group who own at least one credit card. (Round your answers to four decimal places.)

Answer 1

solution:-

given that n = 465

64% in the 18–24 age group

84% in the 25–34 age group

77% in the 35–49 age group

79% in the 50+ age group

the value of 95% confidence from z table is 1.96

confidence interval formula for proportion

=> p +/- z * sqrt(p*(1-p)/n)

(a)

a 95% confidence interval for the proportion of people in the 18–24 age group who own at least one credit card

p = 0.64 , n = 465

=> p +/- z * sqrt(p*(1-p)/n)

=> 0.64 +/- 1.96 * sqrt(0.64*(1-0.64)/465)

=> (0.5964 , 0.6836)

a 95% confidence interval for the proportion of people in the 25–34 age group who own at least one credit card

p = 0.84 , n = 465

=> p +/- z * sqrt(p*(1-p)/n)

=> 0.84 +/- 1.96 * sqrt(0.84*(1-0.84)/465)

=> (0.8067 , 0.8733)

a 95% confidence interval for the proportion of people in the 35–49 age group who own at least one credit card

p = 0.77 , n = 465

=> p +/- z * sqrt(p*(1-p)/n)

=> 0.77 +/- 1.96 * sqrt(0.77*(1-0.77)/465)

=> (0.7317 , 0.8083)

a 95% confidence interval for the proportion of people in the 50+ age group who own at least one credit card

p = 0.79 , n = 465

=> p +/- z * sqrt(p*(1-p)/n)

=> 0.79 +/- 1.96 * sqrt(0.79*(1-0.79)/465)

=> (0.7530 , 0.8270)