Question

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. n = 75, x = 36; 98 percent

Answer 1

Solution :

Given that,

n = 75

x = 36

= x / n =36 /75 = 0.48

1 - = 1 - 0.48 = 0.52

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 * (((0.48 * 0.52) / 75) = 0.1342

A 98 % confidence interval for population proportion p is ,

- E < P < + E

0.48 - 0.1342 < p < 0.48 + 0.1342

0.3458 < p < 0.6142

The 98% confidence interval for the population proportion p is : ( 0.3458 ,  0.6142)