Discussion: Tests for significance

1. Someone gives you a coin and claims that it is a fair coin. Do you believe the claim if
   • you toss it 100 times and get 55 heads?
   • you toss it 100 times and get 75 heads?
   • you toss it 10000 times and get 4000 heads?
2. In our class survey, the mean of the 35 male students' SAT Verbal score is 640, with standard deviation 74. For the 24 female students, the mean is 700 and the standard deviation is 46. We want to find out whether this difference can reasonably be explained by chance variation?
   • If the differences are all due to chance, what do we expect the difference to be?
   • How much spread do the differences have? (standard deviation)
   • How might we estimate the probability of such a difference occuring by chance?
3. In our class survey about smoking habits, of the 26 female students, 18 don't smoke, 8 smoke occasionally and non smoke regularly. Of the 35 male students, 25 don't smoke, 5 smoke occasionally and 5 smoke regularly. We want to find out whether the smoking habits are independent of gender?
   • If they are really independent, what do we expect the numbers to be?
   • How might we measure the difference between our data and the expected data?
   • How might we estimate the probability of such a difference occuring by chance?

Homework