# Analyse some of the statistics of the National Lottery (especially sales information), and see whether there are any trends, similarities, patterns, or correlations in the data.

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Introduction

The National Lottery

Introduction

Aims

The Aims of this Project are:

- To analyse some of the statistics of the National Lottery (especially sales information), and to see whether there are any trends, similarities, patterns, or correlations in the data.
- To check whether some of the statistical variables surrounding the National Lottery fit a known statistical distribution.

How the Statistics Were Collected

The statistics were collected from the Internet. I originally found complete information on the first 187 lottery draws, but decided that this was too many to be easily manageable. Therefore I decided to randomly select 50 draws from this set of information. I used my calculator to generate random numbers from 1 to 187 (without generating previous numbers), and used this to select a final table of data which contained 50 randomly selected lottery draws, which I then sorted by draw number. The data will be reproduced in portions throughout the project. No difficulties in collecting data were encountered.

How the Lottery Works

People who play the lottery pick six different numbers on a ticket from the range 1 to 49. Any person can play the lottery as many times as they like, but each ticket sold counts separately in the final statistics.

Middle

y = 7.288 104 + 0.017x

The best-fit line has been drawn on the scatter diagram in Figure ? and it clearly shows the pattern – as ticket sales increase, in general, so do the number of prize winners

Because the total prize fund depends entirely on the number of sales (as shown in Figure ?, 45% of the revenue generated by people playing the National Lottery goes towards the prize fund), the correlation coefficient for the number of sales and the prize fund should be 1 (if two variables are in direct proportion, the correlation coefficient between them should be 1).

Thus, I checked the correlation coefficient between the number of sales and the prize fund:

H0: The number of sales and the prize fund are in direct proportion (r = 1)

H1: The number of sales and the prize fund are not in direct proportion (r 0).

Sxx = 1.443 1016

Syy = 2.923 1015

Sxy = 6.495 1015

r = = 1

r = 1, I accept H0: There is a direct proportion relationship between ticket sales and total prize fund, as I expected. This is shown on as a scatter diagram in Figure ?, and the diagram in Figure ? is overlaid by a best-fit line, which goes through all the points.

Also if there is

Conclusion

Testing the numbers picked in the 50 draws at the 5% level,

H0: The numbers fit a uniform distribution (they are random).

H1: The numbers do not fit a uniform distribution (they are not random).

Expected number of times each ball is picked =50 = 6.122

See Table ?

= 29.0

Degrees of Freedom = y = 49 – 1 = 48

(5%) = 65.17

29.0 65.17

I do not reject H0: there is no evidence to suggest the selection of the first ball is not random.

Conclusions

The Conclusions drawn from this project are summarised below:

- There is a very significant correlation between the number of lottery winners and the number of ticket sales, as would be expected.
- The total prize fund is in direct proportion to ticket sales, as claimed by Camelot, the lottery operators.
- There is a negative correlation between the first ball picked and the total number of prize winners. The pattern suggests picking high numbers would be a good idea to maximise potential jackpot earnings.
- There is no correlation between the ball set used and the total number of prize winners.
- There is no correlation between the machine used and the total number of prize winners.
- There is no evidence that the selection of the lottery balls is not random.

This student written piece of work is one of many that can be found in our AS and A Level Probability & Statistics section.

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