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kclark36 · #1 June 30th, 2009, 09:37 AM

Here is a problem that I have been working on. I am mixed up on the different testing formulas. I included what i did so far after each question. Thanks for looking

It is suspected that a particular die used in a game of chance was not fair. It was thought that the 1-side was heacy and the 6-side was light. Data was collected concerning the number of observed 1-s when the die was rolled 5000 times. Let p1 equal the probability of rolling a one with that die. We will test the hypothesis H0 p1=1/6 against the alternative hypothesis H1 p1<1/6 (i don't understand why this is < either)

a. give the test statistic and critical region that has an alpha=0.01 significant level

test stat $Z=\frac{Y/5000-1/6}{\sqrt{(1/6*5/6)/5000}}$
crit. reg. $Z \le -z_{0.01}$

b. If y=775 is the observed number of ones in the 5000 rolls, calculate the value of the test statistic and state conclusion about the die

$Z=\frac{775/5000-1/6}{.0052704628}=-2.213594348$

-2.21<-2.36

since -2.21 is not less than -2.36, H0 fails to be rejected

c. find the p-value for this test

$P(Z \le z)=P(Z \le -2.21)=1-0.9864=0.0136=$ ? This part confuses me because of the negative test statistic. I don't know how to calculate the p-value and which way the equality should be facing.

Thanks