Question

3. A gambler was watching a dice game and noticed that one of the dice seemed to come up with a “3” more often than it should. He grabbed the die and rolled it 60 times. He got a “3” 15 times.

a) State the null hypothesis and make the null box. State the alternative hypothesis.

b) Find the z-statistic for testing whether the null hypothesis

c) Find the corresponding P-value. What can you conclude?

Answer 1

Given , n= 60 , x= 15

p (get 3) =15/60 =1/4

Null hypothesis H0 : P= 1/6 that is dice is unbiased

Alternative hypothesis   

let level of significance

  

Z = 5/ 2.8868

Z = 1.732

critical value of Z =1.96

p value =0.0832

Conclusion : since p value 0.0832 > 0.05 also 1.732 < 1.96

Fail to Reject H0

We conclude that dice is unbiased