Question

Study Proves Number Bias in UK Lottery" reported on the internet about a document completed in 2002, "The Randomness of the National Lottery," which was meant to offer irrefutable proof that it was random. But the authors hit a snag when they found that one numbered ball, 38, was drawn so often that they believed there was bias in the selections, perhaps due to a physical difference in the ball: "Haigh and Goldie found that over 637 draws you would expect each number to be drawn between 70 and 86 times. But they found that 38 came up 107 times, 14 times more than the next most drawn ball. 'That is very unusual-the chance is under 1%.  

A. If each number is expected to be drawn between 70 and 86 times, on average how many time is it expected to be drawn?

78

B. Based on your answer to part (A), what proportion of times is each number expected in 637 draws? (Round to the nearest thousandth.)

D. What proportion of the 637 draws did the number 38 come up? (Round to the nearest thousandth.)

E. Find z, the standardized difference between sample proportion (your answer to part [d]) and ideal proportion (your answer to part [b]

Answer 1

A. The calculation of average is 70+86 2 78 B. Ihe proportion of times each expected in 65 / draws is 78 637 0.1224 C. The proportion of number 38 is 107 637 0.1680 D. The calculation of the Z score is p-p p 1-P) 1 0.1680-0.1224 0.1224 1-0.1224) 637 13.5 115