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.

0.404less than<pless than<0.668

B.

0.425less than<pless than<0.647

C.

0.426less than<pless than<0.646

D.

0.405less than<pless than<0.666

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

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z_{0.025 = 1.96}

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

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

= 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