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Answer:
The 99% confidence interval estimate of the percentage of adult Americans aged 18 and older that have donated blood in the past two years is between 16.061% and 20.193%
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
In a survey of 2306 adult Americans aged 18 and older, it was found that 418 of them have donated blood in the past two years.
This means that [tex]n = 2306, \pi = \frac{418}{2306} = 0.18127[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.18127 - 2.575\sqrt{\frac{0.18127*0.81873}{2306}} = 0.16061[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.18127 + 2.575\sqrt{\frac{0.18127*0.81873}{2306}} = 0.20193[/tex]
Confidence interval for the percentage:
Proportions multiplied by 100%. So
0.16061*100% = 16.061%
0.20193 = 20.193%
The 99% confidence interval estimate of the percentage of adult Americans aged 18 and older that have donated blood in the past two years is between 16.061% and 20.193%
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