Assignment 1 is worth 10 marks.

The purpose and intent of the assignment is to help you better understand the relations between three different distributions:

1. the distribution of values in the population,
2. the distribution of values in a sample, and
3. the sampling distribution of the mean.

Think of the 6/49 lottery as sampling from a population (which it really is!). The population would be the balls in the tumbler with the numbers 1 to 49. Balls are drawn one at a time. Once a ball is drawn it cannot be drawn again in that draw. Six balls are draws plus one extra ball. For the purposes of this assignment only the six regular numbers are used. In the lottery, the idea is to match the numbers drawn. In this assignment, we are not interested in matching the numbers but in the mean of the six regular numbers.

The data set consists of the numbers drawn for all the 6/49 draws since the inception of the lottery.The data is found in an Excel spreadsheet on the course website. Each draw consists of seven numbers, six regular numbers and one bonus number. For the purposes of this assignment, we will only consider the regular six numbers.The regular numbers are not reported in the order they were drawn but from smallest to largest. This does not make any difference for our purposes.

Taking sample after sample tells us something about the variability that arises from chance. Here, we are interested in the mean. The mean of the values in a sample is taken as an estimate of the mean of the values in a population.

With all calculations, include the formula that you used.

In all calculations give 4 decimal places.

More samples (draws)

7. There are two Lotto 6/49 draws per week. By next year, there will have been 104 more draws. In five years', there will have been 520 more draws.

1. What difference would taking more samples (viz. more draws) have on the mean, standard deviation, and shape of the distribution of sample means?