Question

In a random sample of 80 people, 52 consider themselves as baseball fans. Compute a 95% confidence interval for the true proportion of people consider themselves as baseball fans and fill in the blanks appropriately. We are 95% confident that the true proportion of people consider themselves as

Answer 1

(0.5455 ; 0.7545)

Explanation:

Given that:

Sample size, n = 80

Baseball fans, x = 52

Proportion, p = x/n = 52 / 80 = 0.65

Using the relation :

Confidence interval :

p ± Zcrit√[(p(1 -p))/n]

Zcrit at 95% = 1.96

Lower boundary: p - Zcrit√[(p(1 -p))/n]

0.65 - 1.96√[(0.65(1 -0.65))/80]

0.65 - 1.96√[(0.65(0.35))/80]

0.65 - 1.96 * √0.00284375

0.65 - (1.96 * 0.0533268)

0.65 - 0.104520528

= 0.545479472

Upper boundary: p + Zcrit√[(p(1 -p))/n]

0.65 + 1.96√[(0.65(1 -0.65))/80]

0.65 + 1.96√[(0.65(0.35))/80]

0.65 + 1.96 * √0.00284375

0.65 + (1.96 * 0.0533268)

0.65 + 0.104520528

= 0.754520528

(0.5455 ; 0.7545)