Question

A study investigated the effectiveness of meditation training in reducing trait anxiety. The study evaluated subjects trait anxiety levels before and after the study subjects participated in an 8 week training course in meditation. The difference in the pre-training and post-training trait anxiety levels were calculated for each participant. For the 27 people in the study, the mean reduction in anxiety was 4.9, and the standard deviation of the reductions was 6.9.
Required:
Find a 99% confidence interval for the population mean.

Answer 1

Answer:

The 99% confidence interval for the population mean reduction in anxiety was (1.2, 8.6).

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-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 = 27 - 1 = 26

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 26 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.99}{2} = 0.995$. So we have T = 2.7787.

The margin of error is:

$M = T\frac{s}{\sqrt{n}} = 2.7787\frac{6.9}{\sqrt{27}} = 3.7$

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 4.9 - 3.7 = 1.2.

The upper end of the interval is the sample mean added to M. So it is 4.9 + 3.7 = 8.6.

The 99% confidence interval for the population mean reduction in anxiety was (1.2, 8.6).