Question

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.

n = 87, x = 26; 98 percent

		(0.185, 0.413)
		(0.202, 0.396)
		(0.184, 0.414)
		(0.203, 0.395)

Answer 1

Solution :

Given that,

n = 87

x = 26

= x / n = 26 /87 = 0.299

1 - = 1 - 0.299 = 0.701

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* (((0.299 * 0.701) / 87) = 0.114

A 98 % confidence interval for population proportion p is ,

- E < P < + E

0.299 - 0.114 < p < 0.299 + 0.114

0.185 < p < 0.413

The 98% confidence interval for the population proportion p is :

( 0.185 < p < 0.413)