normal distribution a level maths help.

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#1
Hi can anyone tell me why I'm wrong with this stats question (Q5). I used the inverse normal function on my calculator to find the critical region and the test value falls outside the critical region so I assumed accept H0. I used sigma=4.3/sqrt40 and mu=11.9 and the the area as 0.025 (half significance level). Thanks in advance.
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#2
Here are the questions and my workings
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1 month ago
#3
(Original post by Harrybeld)
Hi can anyone tell me why I'm wrong with this stats question (Q5). I used the inverse normal function on my calculator to find the critical region and the test value falls outside the critical region so I assumed accept H0. I used sigma=4.3/sqrt40 and mu=11.9 and the the area as 0.025 (half significance level). Thanks in advance.
The variance for a single sample is 4.3, not 4.3^2.
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#4
(Original post by old_engineer)
The variance for a single sample is 4.3, not 4.3^2.
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1 month ago
#5
(Original post by Harrybeld)
Hi can anyone tell me why I'm wrong with this stats question (Q5). I used the inverse normal function on my calculator to find the critical region and the test value falls outside the critical region so I assumed accept H0. I used sigma=4.3/sqrt40 and mu=11.9 and the the area as 0.025 (half significance level). Thanks in advance.
Firstly you made a very common mistake. You were given the variance, not the standard deviation. So you want sqrt(4.3/40).

Secondly, you don't need to find the critical region. All you need is P(mean < 11.2). If this is less than 2.5% then reject H0. Sadly a lot of teachers are themselves really bad when it comes to hypothesis testing.
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#6
(Original post by David Getling)
Firstly you made a very common mistake. You were given the variance, not the standard deviation. So you want sqrt(4.3/40).

Secondly, you don't need to find the critical region. All you need is P(mean < 11.2). If this is less than 2.5% then reject H0. Sadly a lot of teachers are themselves really bad when it comes to hypothesis testing.
Thank you!
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1 month ago
#7
(Original post by David Getling)
Secondly, you don't need to find the critical region. All you need is P(mean < 11.2). If this is less than 2.5% then reject H0. Sadly a lot of teachers are themselves really bad when it comes to hypothesis testing.
The textbooks also don't help. They often find critical regions and standardise when both are not necessary.
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1 month ago
#8
(Original post by Sir Cumference)
The textbooks also don't help. They often find critical regions and standardise when both are not necessary.
Sadly, you are right, and this is such a waste of time, especially in an exam, with extra opportunities to make mistakes.

Also, before the demise of the modular system most students only ever did S1, which didn't include hypothesis testing. Now that they have to do this I'm finding that it's usually very poorly explained, and most students need me to go over it with them in detail.
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1 month ago
#9
(Original post by David Getling)
Also, before the demise of the modular system most students only ever did S1, which didn't include hypothesis testing. Now that they have to do this I'm finding that it's usually very poorly explained, and most students need me to go over it with them in detail.
Also pre-new spec, a significant number of teachers only ever taught stats or mechanics throughout their career. I know a few teachers who struggled a lot initially after the changes because they had never learnt any mechanics/stats past GCSE and now had to teach it at A Level.
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1 month ago
#10
(Original post by Sir Cumference)
Also pre-new spec, a significant number of teachers only ever taught stats or mechanics throughout their career. I know a few teachers who struggled a lot initially after the changes because they had never learnt any mechanics/stats past GCSE and now had to teach it at A Level.
Yep, you are right again. I guess I was really lucky to have a brilliant maths teacher who could teach the lot well, including S level. As a tutor I expect to teach any maths (including further), chemistry or physics topic that students throw at me, and do it off the top of my head. But then I'm an old fossil.
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