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# S2 question 6 mixed excercise 7d help! watch

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1. 6 /C During a garden fete cups of tea are thought to be sold at a rate of 2 every minute. To test this, the number of cups of tea sold suring a random 30 minute interval i srecorded.

Find the critical region for a two tailed hypothesis test that the number of cups of tea sold occurs at a rate of 2 every minute. The probability in each tail should be as close to 2.5% as possible

Ok im really confused it says during a random 30 minute interval so i did 30 x 2 =60 and put lander=60 and tried to use the normal which didnt work out. So i looked at their solution and they got lander=2 and used that to find the critical regions. What im confused about is why have they completely ignored the 30 minute interval bit???
2. (Original post by Ramin Gorji)
...
Your reasoning seems sound, but without seeing their actual question and solution I can't be certain.
3. I also need help with this q pls.

Q. During a garden fete cups of tea are sold at a rate of 2 every minute. To test this, the no. of cups of tea sold during a random 30 minute interval is recorded,.
Find the critical region for a 2 tailed hypothesis that the no. of cups of tea sold occurs at a rate of 2 every minute. The probability in each tail should be as close as possible to 2.5 %.

Book answer: critical region xis greater than or equal to 6. But why is the actual significance 0.0166.

Please could someone very kind teach me the method for this (perhaps using a different example and I can do it on my own? So you're not actually doing my homework for me!). Also don't understand how the 'actual significance' has been calculated.

Thank you
4. To Ramin G. Also stuck on it, but it says 'that the no of cups occrs at a rate of 2 per minute' so isn;t it saying lam. is 2? or am I wrong?
5. (Original post by vet_hopeful!_worried)
I also need help with this q pls.

Q. During a garden fete cups of tea are sold at a rate of 2 every minute. To test this, the no. of cups of tea sold during a random 30 minute interval is recorded,.
Find the critical region for a 2 tailed hypothesis that the no. of cups of tea sold occurs at a rate of 2 every minute. The probability in each tail should be as close as possible to 2.5 %.

Book answer: critical region xis greater than or equal to 6. But why is the actual significance 0.0166.

Please could someone very kind teach me the method for this (perhaps using a different example and I can do it on my own? So you're not actually doing my homework for me!). Also don't understand how the 'actual significance' has been calculated.

Thank you
As near as I can tell (best guess), they have taken a random 1 minute interval, rather than 30 minute interval they claimed.

Then checking the Poisson distribution with lambda = 2, then the closest value to 2.5% (i.e. 0.975 at the upper end) is 0.9834, given a tail of 1-0.9834 = 0.0166 for values of >=6.

God knows how they worked out the bottom end though.
6. Thank you so much. I think they ignore the bottom end, as it is larger than 0.025, that is what I'm 'guessing'. thanks again
7. It's badly worded. It would have been better to state that...

"The probability in each tail should be at most 2.5%"...instead of "as close as possible to".

This would result in exactly one critical region from a 2-tailed test which is very unusual for an S2 question.

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