About binomial distribution

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jaanipola
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#1
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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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(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.
Last edited by grhas98; 1 month ago
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jaanipola
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#3
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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.
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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grhas98
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(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
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jaanipola
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#5
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(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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