MHB Actual vs Expected Number of Lottery Winners

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The discussion centers on the probability of lottery winnings, highlighting that with 50 million tickets purchased, the expected number of jackpot winners is 3.5, while the actual number is 7. The user seeks to determine if a p-value can be calculated to assess whether the actual winners fall within normal expected ranges. A response indicates that a z-test, specifically a one-proportion z-test, is more appropriate than a t-test for this scenario. The conversation emphasizes the need for statistical models to analyze the discrepancy between expected and actual outcomes. Understanding these statistical methods can help clarify the significance of the results.
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Hi,

My maths problem involves probability relating to lotteries.

The odds of winning a lottery jackpot are 1 in 14 million. Over a period of time 50 million tickets have been bought, so the expected number of jackpot winners would be 3.5. However the actual number of jackpot winners is 7.

Is it possible to calculate a p value to prove that although the actual number of winners is higher than expected, it is still within normal expected ranges? Or are there any other statistical models that would answer the question?

I've seen worked examples for calculating the p value where all the outcomes are listed in excel, before applying the T test formula, however I'm not sure how to go about doing this when there are 50 million outcomes!

Thanks,

Paul
 
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fizzypig said:
Hi,

My maths problem involves probability relating to lotteries.

The odds of winning a lottery jackpot are 1 in 14 million. Over a period of time 50 million tickets have been bought, so the expected number of jackpot winners would be 3.5. However the actual number of jackpot winners is 7.

Is it possible to calculate a p value to prove that although the actual number of winners is higher than expected, it is still within normal expected ranges? Or are there any other statistical models that would answer the question?

I've seen worked examples for calculating the p value where all the outcomes are listed in excel, before applying the T test formula, however I'm not sure how to go about doing this when there are 50 million outcomes!

Thanks,

Paul

Hi Paul, welcome to MHB!

We are talking about a proportion here, in which case we don't do a t-test but a z-test.
See for instance the One-proportion z-test in this wiki article.
 
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