Hypothesis Testing AS maths
A restaurant owner notices that her customers typically chose lasagne one fifth of the time. She changes the recipe and believes this will change the proportion of customers choosing lasagne . She takes a random sample of 25 customers
a)find at the 5% significance the critical region for a test to check her belief.
I worked out that
P(X >/ 10 ) = 0.01733 (which is < 0.025 so is the upper critical region)
P(X </ 1 ) = 0.02738
P( X = 0 ) = 0.00377
and I assumed that since the question hasn't mentioned "ensuring the probability is as close as possible to 0.025" that the answer for the lower region would be X = 0 because 0.00377 < 0.025. But the mark scheme says it's (X </ 1) as 0.02738 is closer to 0.025. I thought that you typically took the first value that was lower than 0.025 unless the question specified to take the 'closest possible value' .
Does anyone know if this is a general rule to always take the closest value ...?
a)find at the 5% significance the critical region for a test to check her belief.
I worked out that
P(X >/ 10 ) = 0.01733 (which is < 0.025 so is the upper critical region)
P(X </ 1 ) = 0.02738
P( X = 0 ) = 0.00377
and I assumed that since the question hasn't mentioned "ensuring the probability is as close as possible to 0.025" that the answer for the lower region would be X = 0 because 0.00377 < 0.025. But the mark scheme says it's (X </ 1) as 0.02738 is closer to 0.025. I thought that you typically took the first value that was lower than 0.025 unless the question specified to take the 'closest possible value' .
Does anyone know if this is a general rule to always take the closest value ...?
Original post by zoe2404
A restaurant owner notices that her customers typically chose lasagne one fifth of the time. She changes the recipe and believes this will change the proportion of customers choosing lasagne . She takes a random sample of 25 customers
a)find at the 5% significance the critical region for a test to check her belief.
I worked out that
P(X >/ 10 ) = 0.01733 (which is < 0.025 so is the upper critical region)
P(X </ 1 ) = 0.02738
P( X = 0 ) = 0.00377
and I assumed that since the question hasn't mentioned "ensuring the probability is as close as possible to 0.025" that the answer for the lower region would be X = 0 because 0.00377 < 0.025. But the mark scheme says it's (X </ 1) as 0.02738 is closer to 0.025. I thought that you typically took the first value that was lower than 0.025 unless the question specified to take the 'closest possible value' .
Does anyone know if this is a general rule to always take the closest value ...?
a)find at the 5% significance the critical region for a test to check her belief.
I worked out that
P(X >/ 10 ) = 0.01733 (which is < 0.025 so is the upper critical region)
P(X </ 1 ) = 0.02738
P( X = 0 ) = 0.00377
and I assumed that since the question hasn't mentioned "ensuring the probability is as close as possible to 0.025" that the answer for the lower region would be X = 0 because 0.00377 < 0.025. But the mark scheme says it's (X </ 1) as 0.02738 is closer to 0.025. I thought that you typically took the first value that was lower than 0.025 unless the question specified to take the 'closest possible value' .
Does anyone know if this is a general rule to always take the closest value ...?
If I was doing this question (based on experience of Edexcel and OCR past papers) I would, like you, say that the lower tail is X = 0. However, that's not the only convention. I would suggest checking similar questions from the same source (textbook, exam board or whatever) to see if there is guidance or a consistent pattern.
Original post by zoe2404
A restaurant owner notices that her customers typically chose lasagne one fifth of the time. She changes the recipe and believes this will change the proportion of customers choosing lasagne . She takes a random sample of 25 customers
a)find at the 5% significance the critical region for a test to check her belief.
I worked out that
P(X >/ 10 ) = 0.01733 (which is < 0.025 so is the upper critical region)
P(X </ 1 ) = 0.02738
P( X = 0 ) = 0.00377
and I assumed that since the question hasn't mentioned "ensuring the probability is as close as possible to 0.025" that the answer for the lower region would be X = 0 because 0.00377 < 0.025. But the mark scheme says it's (X </ 1) as 0.02738 is closer to 0.025. I thought that you typically took the first value that was lower than 0.025 unless the question specified to take the 'closest possible value' .
Does anyone know if this is a general rule to always take the closest value ...?
a)find at the 5% significance the critical region for a test to check her belief.
I worked out that
P(X >/ 10 ) = 0.01733 (which is < 0.025 so is the upper critical region)
P(X </ 1 ) = 0.02738
P( X = 0 ) = 0.00377
and I assumed that since the question hasn't mentioned "ensuring the probability is as close as possible to 0.025" that the answer for the lower region would be X = 0 because 0.00377 < 0.025. But the mark scheme says it's (X </ 1) as 0.02738 is closer to 0.025. I thought that you typically took the first value that was lower than 0.025 unless the question specified to take the 'closest possible value' .
Does anyone know if this is a general rule to always take the closest value ...?
Is this from a real past paper? Which one if it is?
Original post by zoe2404
A restaurant owner notices that her customers typically chose lasagne one fifth of the time. She changes the recipe and believes this will change the proportion of customers choosing lasagne . She takes a random sample of 25 customers
a)find at the 5% significance the critical region for a test to check her belief.
I worked out that
P(X >/ 10 ) = 0.01733 (which is < 0.025 so is the upper critical region)
P(X </ 1 ) = 0.02738
P( X = 0 ) = 0.00377
and I assumed that since the question hasn't mentioned "ensuring the probability is as close as possible to 0.025" that the answer for the lower region would be X = 0 because 0.00377 < 0.025. But the mark scheme says it's (X </ 1) as 0.02738 is closer to 0.025. I thought that you typically took the first value that was lower than 0.025 unless the question specified to take the 'closest possible value' .
Does anyone know if this is a general rule to always take the closest value ...?
a)find at the 5% significance the critical region for a test to check her belief.
I worked out that
P(X >/ 10 ) = 0.01733 (which is < 0.025 so is the upper critical region)
P(X </ 1 ) = 0.02738
P( X = 0 ) = 0.00377
and I assumed that since the question hasn't mentioned "ensuring the probability is as close as possible to 0.025" that the answer for the lower region would be X = 0 because 0.00377 < 0.025. But the mark scheme says it's (X </ 1) as 0.02738 is closer to 0.025. I thought that you typically took the first value that was lower than 0.025 unless the question specified to take the 'closest possible value' .
Does anyone know if this is a general rule to always take the closest value ...?
I found this question in the textbook. In an exam they would accept either answer but if it was in an exam they would mention “close as possible” for a question like this.
(edited 1 year ago)
Original post by old_engineer
If I was doing this question (based on experience of Edexcel and OCR past papers) I would, like you, say that the lower tail is X = 0. However, that's not the only convention. I would suggest checking similar questions from the same source (textbook, exam board or whatever) to see if there is guidance or a consistent pattern.
Original post by zoe2404
A restaurant owner notices that her customers typically chose lasagne one fifth of the time. She changes the recipe and believes this will change the proportion of customers choosing lasagne . She takes a random sample of 25 customers
a)find at the 5% significance the critical region for a test to check her belief.
I worked out that
P(X >/ 10 ) = 0.01733 (which is < 0.025 so is the upper critical region)
P(X </ 1 ) = 0.02738
P( X = 0 ) = 0.00377
and I assumed that since the question hasn't mentioned "ensuring the probability is as close as possible to 0.025" that the answer for the lower region would be X = 0 because 0.00377 < 0.025. But the mark scheme says it's (X </ 1) as 0.02738 is closer to 0.025. I thought that you typically took the first value that was lower than 0.025 unless the question specified to take the 'closest possible value' .
Does anyone know if this is a general rule to always take the closest value ...?
a)find at the 5% significance the critical region for a test to check her belief.
I worked out that
P(X >/ 10 ) = 0.01733 (which is < 0.025 so is the upper critical region)
P(X </ 1 ) = 0.02738
P( X = 0 ) = 0.00377
and I assumed that since the question hasn't mentioned "ensuring the probability is as close as possible to 0.025" that the answer for the lower region would be X = 0 because 0.00377 < 0.025. But the mark scheme says it's (X </ 1) as 0.02738 is closer to 0.025. I thought that you typically took the first value that was lower than 0.025 unless the question specified to take the 'closest possible value' .
Does anyone know if this is a general rule to always take the closest value ...?
When determining the critical region for a hypothesis test, the general rule is to choose the values that ensure the probability of Type I error (rejecting the null hypothesis when it is actually true) is below the significance level (in this case, 5%).
In your example, you correctly calculated the upper critical region as P(X >= 10) < 0.025. For the lower critical region, you could choose either P(X <= 0) or P(X <= 1), since both probabilities are less than 0.025.
While there is no hard and fast rule about which value to choose in this situation, it's generally a good idea to choose the value that is closest to the significance level (0.025 in this case), as this will give you the most power to detect a significant difference between the old and new lasagne recipes.
So, in this case, the lower critical region should be P(X <= 1), as this value (0.02738) is closer to 0.025 than P(X = 0) (0.00377). However, it's worth noting that either value would be an acceptable choice for the lower critical region, as both probabilities are below the significance level.
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