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About binomial distribution
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jaanipola
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#1
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 ."
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grhas98
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#2
(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 ."
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 ."
Last edited by grhas98; 1 month ago
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jaanipola
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#3
(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.
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.
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..
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grhas98
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#4
(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..
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..
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jaanipola
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#5
(Original post by grhas98)
Yep that’s correct the null hypothesis should be accepted so there isn’t enough evidence for his claim
Yep that’s correct the null hypothesis should be accepted so there isn’t enough evidence for his claim
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