Question

The Great Eagles of the Misty Mountains wish to estimate the mean number of orcs per raiding party. To do so, they measure the number of orcs in 13 raiding parties. They find an average of 85 orcs per party with a standard deviation of 7.8 orcs in their sample. Compute the 99% confidence interval about the mean number of orcs per raiding party. Answer with the Upper Bound only.

Round to 2 decimal places, as needed.

Answer 1

Answer:

The Upper Bound of the 99% confidence interval about the mean number of orcs per raiding party is of 106.83 orcs per party.

Step-by-step explanation:

We have the standard deviation of the sample, so we use the t-distribution 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 = 13 - 1 = 12

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 12 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.99}{2} = 0.995$. So we have T = 3.0545

The margin of error is:

M = T*s = 3.0545*7.8 = 23.83

In which s is the standard deviation of the sample.

The upper end of the interval is the sample mean added to M. So it is 83 + 23.83 = 106.83 orcs per party.

The Upper Bound of the 99% confidence interval about the mean number of orcs per raiding party is of 106.83 orcs per party.