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 965 and x equals 578 who said​ "yes." Use a 90 % confidence level. Find the best point estimate of the population proportion p. Identify the value of the margin of error E. Construct the confidence interval. Write a statement that correctly interprets the confidence interval. Choose the correct answer below.

Answer 1

Solution :

Given that,

n = 965

x = 578

Point estimate = sample proportion = = x / n = 578/965 = 0.599

1 - = 1-0.599 = 0.401

At 90% confidence level

= 1-0.90% =1-0.90 =0.10

/2 =0.10/ 2= 0.05

Z/2 = Z_{0.05 = 1.645}

Z/2 = 1.645  

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

= 1.645 * ((0.599*(0.401) /965 )

= 0.026

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.599-0.026< p < 0.599+0.026

0.573 < p < 0.625

(0.573 ,0.625 )

The 90% confidence interval for population proportion p is 0.573 and 0.625 .