Respuesta :
Answer:
The margin of error for a 95% confidence interval is of 2.18 hours.
Step-by-step explanation:
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 = 100 - 1 = 99
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 99 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 1.984
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}}[/tex]
In which s is the standard deviation of the sample(square root of the variance) and n is the size of the sample.
In this question:
[tex]s = 11.5, n = 100[/tex]. So
[tex]M = T\frac{s}{\sqrt{n}}[/tex]
[tex]M = 1.984\frac{11}{\sqrt{100}}[/tex]
[tex]M = 2.18[/tex]
The margin of error for a 95% confidence interval is of 2.18 hours.
