Respuesta :
Answer:
a) The margin of error for a 98% confidence interval is of 3.388 people.
b) The 98% confidence interval for the population mean is between 20.61 people and 27.39 people.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the hypergeometric distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 15 - 1 = 14
98% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 14 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.98}{2} = 0.99[/tex]. So we have T = 2.624
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.624\frac{5}{\sqrt{15}} = 3.388[/tex]
In which s is the standard deviation of the sample and n is the size of the sample. This means that the answer to question a is of 3.388.
Question b:
The lower end of the interval is the sample mean subtracted by M. So it is 24 - 3.39 = 20.61 people
The upper end of the interval is the sample mean added to M. So it is 24 + 3.39 = 27.39 people.
The 98% confidence interval for the population mean is between 20.61 people and 27.39 people.
