Question

A survey of 2,306 adult Americans aged 18 or older found that 417 have donated blood in the past two years. The point estimate p-hat = .181, and the sample size n = 2,306. Given the value of LaTeX: \sigmaσσp-hat found in the above question, and with the knowledge that zLaTeX: _{\frac{\alpha}{2}}α 2α 2=1.96 for LaTeX: \alphaαα=.05, Construct a 95% confidence interval for the population proportion of adult Americans aged 18 or older who have donated blood in the past two years. Choose the best answer. Group of answer choices ( .168 , .194 ) ( .165 , .197 ) ( .161 , .201 ) ( .163 , .195 )

Answer 1

Solution :

Given that,

n = 2306

x = 417

Point estimate = sample proportion = = x / n = 417 / 2306 = 0.181

1 - = 1 - 0.181 = 0.819

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025  = 1.96

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

= 1.96 (((0.181 * 0.819) / 2306)

= 0.016

A 95% confidence interval for population proportion p is ,

± E   

= 0.181  ± 0.016

= ( 0.165, 0.197 )