Question

In a survey of 1030 Canadian adults, 720 say that the energy situation in Canada is very or fairly serious.

1. Find the point estimate for the population proportion.

2. Construct a 95% confidence interval for the population proportion.

(a) The critical value:

(b) The margin of error:

(c) The lower limit of the interval:

(d) The upper limit of the interval:

3. find the minimum sample size needed to estimate the population proportion at the 99% confidence level in order to ensure that the estimate is accurate within 3 % of the population proportion.

(a) The critical value:

(b) The margin of error:

(c) The sample size:

Answer 1

Solution :

Given that,

n = 1030

x = 720

1) Point estimate = sample proportion = = x / n = 720 / 1030 = 0.699

1 - = 1 - 0.699 = 0.301

2) a) At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025 = 1.960

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

= 1.96 (((0.699 * 0.301) / 1030)

= 0.028

A 95% confidence interval for population proportion p is ,

± E

= 0.699  ± 0.028

= ( 0.671, 0.727 )

c) lower limit = 0.671

d) upper limit = 0.727

3)a) At 99% confidence level

= 1 - 99%  

= 1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z0.005  = 2.576

b) Margin of error = E = 0.03

c) sample size = n = (Z / 2 / E )2 * * (1 - )

= (2.576 / 0.03)2 * 0.699 * 0.301

= 1551.28

sample size = n = 1552