Question

We observed 28 successes in 70 independent Bernoulli trials. Compute a 90% confidence interval for the population proportion p.

Answer 1

Solution :

n = 70

x = 28

= x / n = 28/ 70 = 0.400

1 - = 1 - 0.400 = 0.600

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

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

= 1.645 * (((0.400 * 0.600) / 70)

= 0.096

A 90 % confidence interval for population proportion p is ,

- E < P < + E

0.400 - 0.096 < p < 0.400 + 0.096

0.304 < p < 0.496

The 90% confidence interval for the population proportion p is : ( 0.304, 0.496)