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# Hypothesis testing poisson s2 watch

1. Could someone help me with this question it's from the cgp s2 edexcel book but I don't have the answers. Samples of pond water have been examined under a microscope by a biologist investigating a particular micro-organism. She found that on average each sample contained 8 of these micro-organisms. She takes a sample from a different pond and is not sure whether the results will be different. There are 15 microorganisms in her first sample. Is this signifcant at the 5% level? So I've got Ho: lambda=8 and H1:lambda >8 what do I do next?
2. (Original post by littlemissnobody)
Could someone help me with this question it's from the cgp s2 edexcel book but I don't have the answers. Samples of pond water have been examined under a microscope by a biologist investigating a particular micro-organism. She found that on average each sample contained 8 of these micro-organisms. She takes a sample from a different pond and is not sure whether the results will be different. There are 15 microorganisms in her first sample. Is this signifcant at the 5% level? So I've got Ho: lambda=8 and H1:lambda >8 what do I do next?
If you're checking for lambda being different to 8, then I'd have thought you'd want a two tailed test, rather than single tailed.

The distribution Po(8) should be available in tables - at least it is in my book.
You'd then want the critical region such that the tails contain 2.5% each.
3. How do I know if it's a one tailed test or two tailed test?
4. (Original post by littlemissnobody)
How do I know if it's a one tailed test or two tailed test?
Because she's concerned whether the result will be different, rather than greater or less than.
5. (Original post by littlemissnobody)
How do I know if it's a one tailed test or two tailed test?
P(X < x1) < 0.025
P (X > x2) < 0.025

You need to find the values of x1 and x2 which satisfy the equalities, using the tables in your book.
6. Oh, I see. But what would the next step be? Is it something like P(x<15)?
7. (Original post by littlemissnobody)
Oh, I see. But what would the next step be? Is it something like P(x<15)?
Nope look at post 5
8. I'm really confused
9. (Original post by littlemissnobody)
I'm really confused
Okay, hypothesis testing can be hard to understand at first, I was completely lost when I started.

It's a bit hard to teach on here and I'm not too good at explaining things.

If you haven't seen s2 videos from examsolutions.co.uk, I would recommend you watch them and then try to attempt the question.

In this question you're trying to find the critical region, where H0 can be rejected and H1 accepted.

The way you find the critical region is by solving the equalities (in post number 5) to find x1 and x2. Then you have to see if 15 is within the critical region, if it is H0 can be rejected, if it's not H0 cannot be rejected.

If you don't understand the concept of 'critical region' I would really recommend you watch the s2 videos on: http://www.examsolutions.net/maths-r.../S2/module.php

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Updated: January 20, 2014
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