Respuesta :
Answer:
The 90% confidence interval for the percentage of people the company contacts who may buy something is between 10.82% and 14%
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].
For this problem, we have that:
[tex]n = 1160, \pi = \frac{144}{1160} = 0.1241[/tex]
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1241 - 1.645\sqrt{\frac{0.1241*0.8759}{1160}} = 0.1082[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1241 + 1.645\sqrt{\frac{0.1241*0.8759}{1160}} = 0.14[/tex]
The 90% confidence interval for the percentage of people the company contacts who may buy something is between 10.82% and 14%
