Question

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

p.

nequals=​56,

xequals=​30;

​95% confidence

A.

0.426less than<pless than<0.646

B.

0.405less than<pless than<0.666

C.

0.425less than<pless than<0.647

D.

0.404less than<pless than<0.668

Answer 1

Solution :

Given that,

n = 56

x = 30

Point estimate = sample proportion = = x / n = 30/56=0.536

1 -   = 1- 0.536 =0.464

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

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

= 1.96 (((0.536*0.464) / 56)

E = 0.131

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.536-0.131 < p < 0.536+0.131

0.405< p < 0.666

correct option b