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SM1 Chapter 7 Hypothesis Testing Edexcel Alevel

Quick question

If it’s a one tailed test do you find the critical region for both upper and lower values, or is it just the lower critical region that needs to be found?
Original post by 2022 g
Quick question

If it’s a one tailed test do you find the critical region for both upper and lower values, or is it just the lower critical region that needs to be found?

if it's one tailed, you're only testing for lower values around the significance level you're given
Reply 2
Original post by orion reid
if it's one tailed, you're only testing for lower values around the significance level you're given

Thank you!
(edited 1 year ago)
Reply 3
Original post by orion reid
if it's one tailed, you're only testing for lower values around the significance level you're given

Seedlings come in trays of 36. On average, 12 seedlings survive to be planted on. A Gardner decides to use a new fertiliser on the seedlings which she believes will improve the number that survive.
Find the critical region at the 10% sig level.
I got
Ho: p=1/3
H1: p>1/3
I went and tested for the lower values around the 10% sig level. And got the critical region being x≤7 because p(x≤7)= 0.0513.. < 0.1
But in the answer they use the upper values around the 10% sig level. How comes?
Original post by 2022 g
Seedlings come in trays of 36. On average, 12 seedlings survive to be planted on. A Gardner decides to use a new fertiliser on the seedlings which she believes will improve the number that survive.
Find the critical region at the 10% sig level.
I got
Ho: p=1/3
H1: p>1/3
I went and tested for the lower values around the 10% sig level. And got the critical region being x≤7 because p(x≤7)= 0.0513.. < 0.1
But in the answer they use the upper values around the 10% sig level. How comes?

So in this question, you're looking at the upper tail not the lower tail so you would use the upper values (you're trying to find evidence that the new fertiliser would improve the number that survive.
if you were finding the lower tail(evidence to say the new fertiliser would reduce the numbers), you would use the lower values which is what you did but that's not what the question is asking.

Therefore, you are trying to test whether the value is greater than 12 which is what would show that the numbers did in fact improve so we use upper values since it would realistically give us values around what we should be expecting and if not we reject the alternative hypothesis.
so here
Ho: p=1/3
H1: p>1/3
test around the 10% SL and use your calculator to find values around 0.9, subtract from one and see if they are above or below the SL
P(X≥16)=1-P(X≤15)= 1-0.8905=0.1095
P(X≥17)=1-P(X≤16)=1-0.9416=0.0584 < 10%
So your critical region would be values greater than or equal to 17 ( we can reject Ho)
HOPE THAT MAKES SENSE!
(edited 1 year ago)
Reply 5
Original post by orion reid
So in this question, you're looking at the upper tail not the lower tail so you would use the upper values (you're trying to find evidence that the new fertiliser would improve the number that survive.
if you were finding the lower tail(evidence to say the new fertiliser would reduce the numbers), you would use the lower values which is what you did but that's not what the question is asking.

Therefore, you are trying to test whether the value is greater than 12 which is what would show that the numbers did in fact improve so we use upper values since it would realistically give us values around what we should be expecting and if not we reject the alternative hypothesis.
so here
Ho: p=1/3
H1: p>1/3
test around the 10% SL and use your calculator to find values around 0.9, subtract from one and see if they are above or below the SL
P(X≥16)=1-P(X≤15)= 1-0.8905=0.1095
P(X≥17)=1-P(X≤16)=1-0.9416=0.0584 < 10%
So your critical region would be values greater than or equal to 17 ( we can reject Ho)
HOPE THAT MAKES SENSE!

“HOPE THAT MAKES SENSE!” yes i understand :grin:
I haven’t done this topic for a really long time. But thanks for helping me recap it xD
Original post by 2022 g
“HOPE THAT MAKES SENSE!” yes i understand :grin:
I haven’t done this topic for a really long time. But thanks for helping me recap it xD

You're welcome, we've all been there honestly. Glad i could help

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