6. (30 points) During a game of chance, an offhand comment by a fellow player le
ID: 3363794 • Letter: 6
Question
6. (30 points) During a game of chance, an offhand comment by a fellow player leads you to suspect foul play. In particular, you suspect the red die is biased towards an outcome of one. So far this game, out of 100 total rolls, you have rolled a one 20 times. a. Use the above information to develop a null and alternate hypothesis regarding the fairness of the die with regard to an outcome of one b. Identify and compute a sample statistic from vour observed rolls c. Find the p.value associated with your sample statistic. d. Evaluate your null hypothesis at a significance level = 0.05. What can you say about Ho?Explanation / Answer
Given that,
possibile chances (x)=20
sample size(n)=100
success rate ( p )= x/n = 0.2
success probability,( po )=0.16667
failure probability,( qo) = 0.83333
null, Ho:p=0.16667
alternate, H1: p!=0.16667
level of significance, = 0.05
from standard normal table, two tailed z /2 =1.96
since our test is two-tailed
reject Ho, if zo < -1.96 OR if zo > 1.96
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.2-0.16667/(sqrt(0.1388911111)/100)
zo =0.8943
| zo | =0.8943
critical value
the value of |z | at los 0.05% is 1.96
we got |zo| =0.894 & | z | =1.96
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 0.89433 ) = 0.37115
hence value of p0.05 < 0.3711,here we do not reject Ho
ANSWERS
---------------
null, Ho:p=0.16667
alternate, H1: p!=0.16667
test statistic: 0.8943
critical value: -1.96 , 1.96
p-value: 0.37115
decision: do not reject Ho
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