Question

431/633 animals have brown fur. The rest don't. Estimate the proportion of animals who have brown fur. Total population of 300,000,000.

In addition, find 90% confidence interval representing the entire proportion of brown fur animals.

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 432 / 633 = 0.682

1 - = 1 - 0.682 = 0.318

Z_/2 = 1.645

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

= 1.645 * (((0.682 * 0.318) / 633)

= 0.030

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.682 - 0.030 < p < 0.682 + 0.030

0.652 < p < 0.712

The 90% confidence interval for the population proportion p is : 0.652 , 0.712