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Hypothesis testing, significance level.

Dewi, a candidate in an election, believes that 45% of the electorate intend to vote for
him. His agent, however, believes that the support for him is less than this. Given that
p denotes the proportion of the electorate intending to vote for Dewi,
They decide to question a random sample of 60 electors. They define the critical region to be X ≤ 20, where X denotes the number in the sample intending to vote
for Dewi.
(b) (i) Determine the significance level of this critical region.

I know that Under H0, X is B(60,0.45).
Sig level = P(X ≤ 20)
= 0.0446 (ANSWER)

But my binomial distribution table only goes up to N=50 when this is N=60, I can do the calculator method but i wanted to know the non calculator method too. So can someone please tell me how. I know you have to do the opposite but i still don't get the correct answer.
(edited 5 years ago)
Original post by kurro
Dewi, a candidate in an election, believes that 45% of the electorate intend to vote for
him. His agent, however, believes that the support for him is less than this. Given that
p denotes the proportion of the electorate intending to vote for Dewi,
They decide to question a random sample of 60 electors. They define the critical region to be X ≤ 20, where X denotes the number in the sample intending to vote
for Dewi.
(b) (i) Determine the significance level of this critical region.

I know that Under H0, X is B(60,0.45).
Sig level = P(X ≤ 20)
= 0.0446 (ANSWER)

But my binomial distribution table only goes up to N=50 when this is N=60, I can do the calculator method but i wanted to know the non calculator method too. So can someone please tell me how. I know you have to do the opposite but i still don't get the correct answer.


The only non-calculator way would be to find a table that does go up to n = 60.
Original post by kurro


I know that Under H0, X is B(60,0.45).
Sig level = P(X ≤ 20)
= 0.0446 (ANSWER)

But my binomial distribution table only goes up to N=50 when this is N=60, I can do the calculator method but i wanted to know the non calculator method too. So can someone please tell me how. I know you have to do the opposite but i still don't get the correct answer.


You could use the Normal approximation to the Binomial distribution for such a large n.
Original post by Prasiortle
The only non-calculator way would be to find a table that does go up to n = 60.


The table my exam board gives in the exams only go up to n=50 :frown:
Original post by kurro
The table my exam board gives in the exams only go up to n=50 :frown:


In that case, an approximation could be used as Gregorius above has stated.
Original post by kurro
The table my exam board gives in the exams only go up to n=50 :frown:


In that case, an approximation could be used, as Gregorius above has stated.
Original post by Gregorius
You could use the Normal approximation to the Binomial distribution for such a large n.


Original post by Prasiortle
In that case, an approximation could be used, as Gregorius above has stated.


How would you do that?
Original post by kurro
How would you do that?


The mean is np and the variance is npq

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