Question

In a random sample of 192 packages shipped by air freight, 31 had some damage. Construct a 95% confidence interval for the true proportion of damaged packages using the large sample confidence interval formula. zα 1.282 1.645 1.960 2.326 2.576 3.090 α(tail area) 0.1 0.05 0.025 0.01 0.005 0.001 %ile 90 95 97.5 99 99.5 99.9 Your answers can be rounded to three decimal digit accuracy when entered.

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 31 / 192 = 0.161

1 - = 0.839

Z_/2 = 1.96

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

= 1.96 * (((0.161 * 0.839) / 192)

= 0.052

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.161 - 0.052 < p < 0.161 + 0.052

0.109 < p < 0.214

(0.109 , 0.214)