Answer: aA 90% confidence interval for the population proportion of adults in the U.S. who have donated blood in the past two years = (0.163,0.189)
Step-by-step explanation:
Let p = population proportion of adults in the U.S. who have donated blood in the past two years.
Given: A Gallup survey of 2322 adults (at least 18 years old) in the U.S. found that 408 of them have donated blood in the past two years.
Sample size: n= 2322
Sample proportion [tex]q=\dfrac{408}{2322}=0.176[/tex]
Critical z-value for 90% confidence level : z*=1.645
The confidence interval for population proportion:
[tex]q\pm z^*(\sqrt{\dfrac{q(1-q)}{n}})[/tex]
A 90% confidence interval for the population proportion of adults in the U.S. who have donated blood in the past two years:
[tex]0.176\pm (1.645)(\sqrt{\dfrac{0.176(1-0.176)}{2322}})\\\\=0.176\pm (1.645)(0.0079)\\\\=(0.176\pm0.013)\\\\=(0.176-0.013,0.176+0.013))\\\\=(0.163,0.189)[/tex]
Hence,
