Question

1. Roll the die 40 times and record the rolled values in the table below. These represent 40 observations of X. 2. Calculate the sample mean of your 40 rolls using Excel. This number represents a single observation of the random variable X (which, again, is a random variable representing the sample mean of 40 rolls of a die). Record the value for the sample mean in the space below: Sample Mean Observation (= first observation of X):

Answer 1

1.

A die is rolled 40 times and the values are recorded as below:

3	6	5	3	5	6	1	4
4	5	6	2	5	4	1	2
4	5	5	1	1	3	3	2
1	5	2	5	3	4	5	2
1	1	5	6	3	3	5	6

2.

Using excel we find the sample mean of the above 40 observations. The excel code is :

=AVERAGE(number1,number2,...number40)

We get the sample mean as 3.575

Therefore, sample mean of observation = 3.575

4.

We cannot expect to get the same value of x̅ each time we roll the die 40 times because the outcome of throwing the die is random and we get different samples each time. So, the sample mean will also change from trial to trial because it is calculated as the sum of observations divided by 40 and the sum of observations will vary each time.