Question

In a survey of 520 potential jurors, one study found that 360 were regular watchers of at least one crime-scene forensics television series.

(a) Assuming that it is reasonable to regard this sample of 520 potential jurors as representative of potential jurors in the United States, use the given information to construct a 95% confidence interval for the true proportion of potential jurors who regularly watch at least one crime-scene investigation series.

Answer 1

Solution :

Given that,

n =520

x = 360

Point estimate = sample proportion = = x / n = 360/520=0.692

1 -   = 1- 0.692 =0.308

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

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

= 1.96 (((0.692*0.308) / 520)

E = 0.040

A 95% confidence interval for proportion p is ,

- E < p < + E

0.692-0.040 < p < 0.692+0.040

0.652< p < 0.732

(0.652 , 0.732)