Question

Suppose someone has told you that he will pay you $500 if you can roll a die and have it land on a 6. You both agree that you will use a virtual die that can be found at this website. Be sure to set it on one die, and not two. You are not certain that using a die such as this virtual die is actually as fair as a normal plastic die and want to justify for yourself that this die does not land on one face more often than any other face. In other words, it would be a terrible thing if this die landed on a 6, fewer times than it landed on any of the other five faces. After all, how can a computer ever be random? It is not like the computer is actually rolling a die. You perform a hypothesis test to see if a computer can be random. So, the question you are asking yourself is this: Does this die land on 6 as often as it lands on any other number? Or, said in a manner that would help you with your null and alternate hypotheses, Does this die land on a six 1/6 (0.167) of the time? You decide to flip the die 50 times and record the number of times the die lands on a 6 out of that 50 times.

#### i did the die and i got the face of 6 (13 times out of 50)

Set up your study: Tell me first what each of following represents; then

H0= p-hat = 1/6 , H1: p-hat= not 1/6

n= 50 p=1/6 ,

a= 0.5

1      Explain to me , what this test statistic is telling you. (In other words, what does a z score tell you?)

2         Is this test statistic beyond either one of your critical values? In other words, is this test statistic further to the left of your left-hand critical value, or, is it to the right of your right-hand critical value? Explain.

3.         What is the p-value for this result – In other words operating under the assumption that H₀ is true, how likely is it that we would have seen a   value was as far to the left or right as it was; that is what the p-value is.

4         What is your decision? Be sure to give me your reasoning using both the critical value method and the p-value method. (Obviously, normally, you only have to provide reasoning using one method, not two.)

            Decision: _________________

                 Reason using the critical value method? Explain.

                 Reason using the p-value method? Explain.

5        What is your conclusion? (In other words, how do you feel about using this online die based upon your statistical test?)

         Conclusion:

6.       Finally, assume you are doing the roll for the $500. On what face did the die land? Would you have won the $500 prize?

Answer 1

1)Z score tells us how many standard deviations away is the point estimate from the mean of the mean.

2)We are testing at 5% significance level. Hence critical values=-1.96 and 1.96

Our test statistic is between both the critical values.

3)pvalue=2*P(Z>1.771)=0.0766

4)Decision ->Fail to reject H0

Reason using critical value method->The test statistic is not greater than the extreme values but is instead between the two critical values

Reason using pvalue->the pvalue>0.05

5)Conclusion->Fail to reject H0 and we say the virtual die is not biased

6)The die would have an equal probability across all the sides. Hence, there is a 1/6th probabiity of winning 500.