Posted by ester sanderson on Sunday, October 4, 2009 at 11:13pm.
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(1-π0)>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(1-π0)/n)
=sqrt((1/6)(5/6)/60)
=0.048
z=(p-π0)/σp
=(9/60-1/6)/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.