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About binomial distribution

Can anyone help me how to solve this problem. I am very confused. The question is "A clairvoyant claims that he can tell the suit of any card drawn randomly from a pack of 52 cards. In a test he succeeds 4 out of 6 cards . Carry out a test at a 2.5 percent signifance level to see whether his claim is realistic or not ."
Original post by jaanipola
Can anyone help me how to solve this problem. I am very confused. The question is "A clairvoyant claims that he can tell the suit of any card drawn randomly from a pack of 52 cards. In a test he succeeds 4 out of 6 cards . Carry out a test at a 2.5 percent signifance level to see whether his claim is realistic or not ."


You need to set up a hypothesis test with a binomial distrobution. The null hypothesis would be that he cannot tell the suit of any card. As there are 4 suits the null hypothesis will assume p=0.25 and therefore H1: p>0.25. You are given n the number of tests, x the number of successes so with this you can calculate the probability with P(X >= x)~B(p,n) and either accept or reject the null hypothesis.
(edited 1 year ago)
Reply 2
Avatar for jaanipola
jaanipola
OP
6
Original post by grhas98
You need to set up a hypothesis test with a binomial distrobution. The null hypothesis would be that he cannot tell the suit of any card. As there are 4 suits the null hypothesis will assume p=0.25 and therefore H1: p>0.25. You are given n the number of tests, x the number of successes so with this you can calculate the probability with P(X >= x)~B(p,n) and either accept or reject the null hypothesis.


Thanks for reply
I just tried to solve this problem according to your method
n =6
P=0.25
x=4
P( x>=4) = 1- p( x<= 3 ) =1-0.962...=0.037..=3.76% it is greater than 2.5 level so I think it means his claim is false. Null hypothesis says he cannot tell suit of any card so does it mean null hypothesis accept ? Thanks..
Original post by jaanipola
Thanks for reply
I just tried to solve this problem according to your method
n =6
P=0.25
x=4
P( x>=4) = 1- p( x<= 3 ) =1-0.962...=0.037..=3.76% it is greater than 2.5 level so I think it means his claim is false. Null hypothesis says he cannot tell suit of any card so does it mean null hypothesis accept ? Thanks..


Yep that’s correct the null hypothesis should be accepted so there isn’t enough evidence for his claim
Reply 4
Avatar for jaanipola
jaanipola
OP
6
Original post by grhas98
Yep that’s correct the null hypothesis should be accepted so there isn’t enough evidence for his claim

Thanks

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