Question

Use the sample data and confidence level given below to complete parts​ (a) through​ (d). A research institute poll asked respondents if they felt vulnerable to identity theft. In the​ poll, n equals n=935 and x equals x=517 who said​ "yes." Use a 95% confidence level.

Answer 1

Solution :

Given that,

n = 935

x = 517

Point estimate = sample proportion = = x / n = 517/935=0.553

1 - = 1-0.553=0.447

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

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

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

= 1.96 (((0.553*0.447) / 935)

= 0.0319

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.553-0.0319 < p <0.553+ 0.0319

0.5211< p < 0.5849

The 95% confidence interval for the population proportion p is : 0.5211, 0.5849