Question

According to a survey of 667 small business participants chosen at random in the Constant Contact Small Biz Council in May of 2013, 400 of the respondents say it is harder to run a small business now than it was 5 years ago. When estimating the population proportion, what is the 99% confidence interval estimating the proportion of businesses who believe it is harder to run a business now than 5 years ago?

Answer 1

Solution :

Given that,

n = 667

x = 400

Point estimate = sample proportion = = x / n = 400/667=0.600

1 -   = 1-0.600 =0.400

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576 ( Using z table )

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

= 2.576* (((0.600*0.400) / 667)

E = 0.0489

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.600-0.0489 < p < 0.600+0.0489

0.5511< p < 0.6489

The 99% confidence interval for the population proportion p is : 0.5511, 0.6489