Question

You may need to use the appropriate appendix table or technology to answer this question.

A simple random sample of 400 individuals provides 128 Yes responses.

(a)

What is the point estimate of the proportion of the population that would provide Yes responses?

(b)

What is your estimate of the standard error of the proportion,

σ_p?

(Round your answer to four decimal places.)

(c)

Compute the 95% confidence interval for the population proportion. (Round your answers to four decimal places.)

to

Answer 1

Solution :

Given that,

n = 400

x = 128

a)

= x / n = 128 / 400 = 0.32

1 - = 1 - 0.32 = 0.68

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

b)

Standard error of the proportion = [( * (1 - )] / n)

                                              = 0.0342

c)

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

= 1.96 * ([(0.32 * 0.68] / 400)

= 0.0457

A 95% confidence interval for population proportion p is ,

- E < P < + E

0.32 - 0.0457 < p < 0.32 + 0.0457

0.2743 < p < 0.3657

(0.2743, 0.3657)