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This is a summary of part of the lesson on 9th February 04: Task 2 the bullets.
The formulas we will use can be found on a page at Tufte University. There are better tutorials around and I'll put a few here when I find some.
We can use a formal statistical test to decide if the old 1p coins we measured the rim thickness of really are thinner than the new (2003) coins.
| old | new | |
| N | 13 | 14 |
| mean | 1.49mm | 1.70mm |
| SD | 0.13mm | 0.03mm |
Data summary above was for the coin task - I used Georgina's summary of the data we took on the lesson - the main difference will be which group you put the 1996 coin in!
| Stage in general process | Specific example of coins data |
| State the null hypothesis | "There is no difference between the new and old coins" |
| Decide on the significance level to adopt in the test | 5% corresponds to a 1 in 20 chance of a 'significant' result occurring when in fact there is no difference. Look up 'type I' and 'type II' errors in a textbook. |
| Calculate the statistics as dictated by the type of data and number of variables: Different situations call for different statistics |
Calculate the mean, standard deviation, for the 'new' and the 'old' coins.
Calculate the 95% confidence interval of the difference of the means |
| Accept or reject the null hypothesis according to the statistical criteria adopted |
If the confidence interval includes zero then you have to accept the null hypothesis
If the confidence interval does not include zero then you have to reject the null hypothesis and you can conclude that there is a difference between 'old' and 'new' coins |
Details of the calculations soon!
--
Keith Burnett
Last modified: 2004-02-09