Respuesta :
Answer:
The 95% confidence interval for the percent of all coffee drinkers who would say they are addicted to coffee is between 21% and 31%.
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].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
A confidence interval has two bounds, the lower and the upper
Lower bound:
[tex]\pi - M[/tex]
Upper bound:
[tex]\pi + M[/tex]
In this problem, we have that:
[tex]\pi = 0.26, M = 0.05[/tex]
Lower bound:
[tex]\pi - M = 0.26 - 0.05 = 0.21[/tex]
Upper bound:
[tex]\pi + M = 0.26 + 0.05 = 0.31[/tex]
The 95% confidence interval for the percent of all coffee drinkers who would say they are addicted to coffee is between 21% and 31%.
