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,

#### 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 H_{0} 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.

topic: if someone asked you what you ahoulf be willing to pay for a
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a 1,2, pr 6 came up, or $0 if a 4 or 5 came up. How would you
approach figuring this out?
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