Pedro thinks that he has a special relationship with the num

Pedro thinks that he has a special relationship with the number 3. In particular, Pedro thinks that he would roll a 3 with a fair 6-sided die more often than you\'d expect by chance alone. Suppose p is the true proportion of the time Pedro will roll a 3.

(a) State the null and alternative hypotheses for testing Pedro\'s claim. (Type the symbol \"p\" for the population proportion, whichever symbols you need of \"<\", \">\", \"=\", \"not =\" and express any values as a fraction e.g. p = 1/3)
H 0   = ______________
H a   = ______________

(b) Now suppose Pedro makes n = 30 rolls, and a 3 comes up 6 times out of the 30 rolls. Determine the P-value of the test:
P-value =______________

Solution

a)
Under The Null Hypothesis H0:P=0.1667
Under The Alternate Hypothesis H1: P!=0.1667
Test Statistic
No. Of Success chances Observed (x)=6
Number of objects in a sample provided(n)=30
No. Of Success Rate ( P )= x/n = 0.2
Success Probability   ( Po )=0.1667
Failure Probability ( Qo) = 0.8333
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.2-0.1667/(Sqrt(0.13891111)/30)
Zo =0.49
b)
P-Value: Two Tailed ( double the one tail ) - Ha : ( P != 0.48937 ) = 0.62458