Question

Use the given data to construct a confidence interval of the requested level. x = 113, n = 176, confidence level 98% Group of answer choices 0.558 < p < 0.726 0.571 < p < 0.713 0.446 < p < 0.838 0.606 < p < 0.678

Answer 1

Solution :

Given that,

n = 176

x = 113

Point estimate = sample proportion = = x / n = 113/176=0.642

1 -   = 1- 0.642 =0.358

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02/ 2 = 0.01

Z/2 = Z0.01 = 2.326 ( Using z table    )

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

= 2.326 (((0.642*0.358) / 176)

E = 0.0841

A 98% confidence interval for population proportion p is ,

- E < p < + E

0.642-0.0841 < p <0.642+ 0.0841

0.558< p < 0.726

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