statistics
posted by ester sanderson .
If a dice is rolled one time, classical probability would indicate that the probability of a "two" should be 1/6. If the dice is rolled 60 times and comes up "two" only 9 times does that suguest that the dice is loaded? why or why not

A hypothesis related to the population proportion will be tested. In this case,
Theoretical proportion, π0 = 1/6,
number of observations, n = 60
Observed proportion, p = 9/n = 9/60
In the case where n>30, nπ0>5 and n(1π0)>5, the normal distribution could be used as an approximation for the test of the null hypothesis, H0, where
H0 : the sample proportion, π = 1/6.
The sample standard error, σp
=sqrt(π0(1π0)/n)
=sqrt((1/6)(5/6)/60)
=0.048
z=(pπ0)/σp
=(9/601/6)/0.048
=0.347
critical z (α=0.05)=1.645 (from the Normal distribution table).
Since 0.347 is greater than 1.645, the null hypothesis is not rejected at the 5% level of significance, i.e. there is no indication that the die is loaded. 
Find the chance that if you toss a pair of dice, you get 6 for the sum.