Question

A study involves 605 randomly selected deaths, with 28 of them caused by accidents. Use this data to construct a 98% confidence interval for the true percentage of all deaths that are caused by accidents.

Answer 1

Solution :

Given that,

n = 605

x = 28

Point estimate = sample proportion = = x / n = 605 / 28 = 0.046

1 - = 1 - 0.046 = 0.954

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02 / 2 = 0.01

Z_/2 = Z _0.01 = 2.326

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

= 2.326 * (((0.046*0.954) / 605)

= 0.020

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.046 - 0.020 < p < 0.046 + 0.020

0.026 < p < 0.066

The 98% confidence interval for the true percentage of all deaths that are caused by accidents is : (0.026 , 0.066 )