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a level maths hypothesis testing q

Seedlings come in trays of 36. On average, 12 seedlings survive to be planted on. A gardener
decides to use a new fertiliser on the seedlings which she believes will improve the number
that survive.

State the probability of incorrectly rejecting H0 using this critical region

I know how to find the critical region but don't quite get the question.
Reply 1
Original post by quickquestion805
Seedlings come in trays of 36. On average, 12 seedlings survive to be planted on. A gardener
decides to use a new fertiliser on the seedlings which she believes will improve the number
that survive.

State the probability of incorrectly rejecting H0 using this critical region

I know how to find the critical region but don't quite get the question.


You should know the null hypothesis probability and from a quick google its a 90%/10% significance level, though your question may be slightly differet It doesnt explicitly state it, but I guess theyre presuming the test is on a single tray.

What are you unsure about? Can you post a pic of the full quesition as the question seems to be missing either the level or the critical region.
(edited 10 months ago)
Original post by mqb2766
You should know the null hypothesis probability and from a quick google its a 90%/10% significance level, though your question may be slightly differet It doesnt explicitly state it, but I guess theyre presuming the test is on a single tray.

What are you unsure about? Can you post a pic of the full quesition.


Screenshot 2023-06-22 083831.png
my bad, accidentally left out the significance level. I was confused about the final bit, 'State the probability of incorrectly rejecting H0 using this critical region'. Are they simply asking for the actual significance level? I guess I'm just unsure about the wording of the question and perhaps the meaning of actual significance level.
(edited 10 months ago)
Reply 3
Original post by quickquestion805
Screenshot 2023-06-22 083831.png
my bad, accidentally left out the significance level. I was confused about the final bit, 'State the probability of incorrectly rejecting H0 using this critical region'. Are they simply asking for the actual significance level? I guess I'm just unsure about the wording of the question and perhaps the meaning of actual significance level.

what did you get for b?
Original post by mqb2766
what did you get for b?

X is greater than or equal to 17
Reply 5
Original post by quickquestion805
X is greater than or equal to 17


Agree with that. However, thats not a 10% significance level as the random variable is discrete, so there is a bit less than 10% chance of incorrectly rejecting the null hypothesis using that critical region.

10% level corresponds to a 10% chance of incorrectly rejecting the null hypothesis, a so called type 1 error, when you have a continuous random variable.
(edited 10 months ago)
Original post by mqb2766
Agree with that. However, thats not a 10% significance level as its discrete, so there is a bit less than 10% chance of incorrectly rejecting the null hypothesis using that critical region.

10% level means there is 10% chance of incorrectly rejecting the null hypothesis - a so called type 1 error.


That makes sense. I was just confused about the 'incorrectly' bit in the definition of significance level, but I googled it. Thank you for the help

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