Question

In a survey of 1060 Canadian adults, 770 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 5 % of the population proportion.

(a) The critical value:

(b) The margin of error:

(c) The sample size:

Answer 1

Solution :

Given that,

n = 1060

x = 770

1) Point estimate = sample proportion = = x / n = 770 / 1060 = 0.726

1 - = 1 - 0.726 = 0.274

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 (((0.726 * 0.274) / 1060 )

= 0.027

A 95% confidence interval for population proportion p is ,

c) lower limit = - E

lower limit = 0.726 - 0.027

lower limit = 0.699

d) upper limit = + E

upper limit = 0.726 + 0.027

upper limit = 0.753

3) a) At 99% confidence level

= 1 - 99%  

= 1 - 0.99 =0.01

/2 = 0.05

Z/2 = Z0.005  = 2.576

b) margin of error = E = 0.05

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

= (2.576 / 0.05 )2 * 0.726 * 0.274

= 528.006

sample size = n = 529