Question

When 385 junior college students were surveyed, 185 said they have a passport. Construct a 95% confidence interval for the proportion of junior college students that have a passport. Round to the nearest thousandth. Interpret your answer in terms of the application.

Answer 1

Solution :

Given that,

n = 385

x = 185

Point estimate = sample proportion = = x / n = 185/385=0.481

1 -   = 1- 0.481 =0.519

At 95% confidence level

  = 1 - 95% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 1.96 ( Using z table )

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

= 1.96 (((0.481*0.519) /385 )

= 0.050

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.481-0.050 < p < 0.481+0.050

0.431< p < 0.531