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 994 and x equals 526 who said​ "yes." Use a 90 % confidence level. LOADING... Click the icon to view a table of z scores. ​a) Find the best point estimate of the population proportion p. 0.529 ​(Round to three decimal places as​ needed.) ​b) Identify the value of the margin of error E. Eequals 0.026 ​(Round to three decimal places as​ needed.) ​c) Construct the confidence interval. nothingless than p less than nothing ​(Round to three decimal places as​ needed.) I need another portion of this question answered please. thank you

Answer 1

Solution :

Given that,

n = 994

x = 526

Point estimate = sample proportion = = x / n = 526 * 994 = 0.529

1 - = 1 - 0.529 = 0.471

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z _0.05 = 1.645

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

= 1.645 * (((0.529 * 0.471) / 994)

= 0.026

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.529 - 0.026 < p < 0.52 9+ 0.026

0.503 < p < 0.555

The 90% confidence interval for the population proportion p is : (0.503 , 0.555)