Question

A random sample of 320 college students were asked if they believed that places could be haunted and 80 responded yes. Estimate the true proportion of college students who believe in the possibility of haunted places with 99% confidence.

Answer 1

Solution :

Given that,

n = 320

x = 80

Point estimate = sample proportion = = x / n = 80/320=0.25

1 -   = 1- 0.25 =0.75

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* (((0.25*0.75) /320 )

E = 0.0624

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.25-0.0624 < p < 0.25+0.0624

0.1876< p < 0.3124

The 99% confidence interval for the population proportion p is : 0.1876,0.3124

Point estimate = true proportion = = 0.25