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# AQA A2 Mathematics MS2B Statistics 2B - 21st June 2016

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1. Thank u so much
Can u explain type I and type II as well pls
2. (Original post by salome12)
Basically whenever we 'accept H0', we never prove u=20 (or whatever it is), it just means that we show there isn't enough evidence to disprove u=20 .

When we 'reject H0', we say 'there is statistically significant/enough evidence' to disprove H0.

like if you carried out a 5% significance test and you reject H0, that means "there is enough evidence at a 5% level to disprove H0".
If you then did a 1% significance test and accept H0, that means "there is not enough evidence at a 1% level to disprove H0".
is this the same with contingency tables??
is this the same with contingency tables??
yeah
if you reject H0 , 'there is significant evidence to suggest an association between X and Y'
if you accept H0, 'there is insufficient evidence to prove there is an association between X and Y'
4. Quick question,
If I'm not given sigma, I need to find an unbiased estimator for s which means I use a t-distribution rather than a z distribution?? Unless the sample size is large enough?
5. (Original post by yoda123)
Thank u so much
Can u explain type I and type II as well pls
Type I
Null hypothesis is rejected when it is actually true.

Type II
Null hypothesis is not rejected (accepted) when it is actually false.

We could also be asked about the probability of making a Type I error. All you need to do in this case is state the significance level used in the hypothesis test.
6. (Original post by 09craige)
Quick question,
If I'm not given sigma, I need to find an unbiased estimator for s which means I use a t-distribution rather than a z distribution?? Unless the sample size is large enough?
Yup
7. (Original post by 09craige)
Quick question,
If I'm not given sigma, I need to find an unbiased estimator for s which means I use a t-distribution rather than a z distribution?? Unless the sample size is large enough?
If the variance of the population, , is unknown then we use the Student's t-distribution unless the sample size is large enough for the central limit theorem to be applied, in which case we use the standard normal distribution.
8. I dont get cumulative and probability density functions does anyone have any notes on that
9. (Original post by yoda123)
I dont get cumulative and probability density functions does anyone have any notes on that
The integral of (area underneath) a probability density function, , over a certain range gives the probability of a continuous random variable taking a value in that range. It's important to understand that is non-negative for all , and the total area underneath the function is always 1.

A cumulative distribution function, , gives the probability that a random variable, , will be less than or equal to a particular value, . Essentially, this is the area underneath the p.d.f from up to that value. Note also that is increasing and continuous.
10. When is it we need to use standard error? I know its when its for a sample, but what if the standard deviation of the sample is known, do we still use it ?

And what if it isnt standard error ?
11. (Original post by Roxanne18)
When is it we need to use standard error? I know its when its for a sample, but what if the standard deviation of the sample is known, do we still use it ?

And what if it isnt standard error ?
Be careful not to confuse samples and populations. We can always find the standard deviation of a sample very easily, it is the standard deviation of the population which may be unknown.

Essentially, the standard error of the sample mean helps us estimate how far the sample mean is from the population mean. We use it to calculate confidence intervals for the population mean using sample data.
12. when calculating s.d, do you use n when the sample is large (like 40) and n-1 when sample is small (less than 30) ?
13. (Original post by salome12)
Yup
This has confused me, according to my book the only time you use t is when you know the distribution is normal and the variance is unknown. That right hand branch doesn't apply if the distribution isn't known to be normal, right?
14. Hope it goes better than core 3. Good luck guys.
15. (Original post by -jordan-)
This has confused me, according to my book the only time you use t is when you know the distribution is normal and the variance is unknown. That right hand branch doesn't apply if the distribution isn't known to be normal, right?

the student's t distribution is normal too, it just gives critical values that account for more error.

Basically if n is large we use CLT to assume it is normal
but if n is small, we must be told the distribution is normal

if we are told population sd, we use normal distribution with z

if we are not told the population s.d and n is large, we use the sample estimate for sd (which is a good estimate) and use the normal distribution with z values

if we are not told the population sd and n is small, we use the sample estimate for the sd (which is 'bad' estimate) and the student's t distribution (to account for error in sample sd)

since we only use student's t when n is small , we must be told the distribution is normal
16. Good luck guys!
17. (Original post by KB_97)
Hope it goes better than core 3. Good luck guys.
(Original post by student0042)
Good luck guys!
Good luck!
18. They couldn't possibly ask us to use the clt right. I'm panicking that they're gonna throw in as stuff which I haven't revised.
19. (Original post by KB_97)
They couldn't possibly ask us to use the clt right. I'm panicking that they're gonna throw in as stuff which I haven't revised.
If the population mean is unknown, and our sample size is large (n>30), then we make use of the Central Limit Theorem. The working in this case is no different to when we know the population mean, just use a z statistic.

I don't think they will ask us to talk about the theorem itself, but we are expected to be able to apply it.
20. Any workings for the last question? Realized I had the wrong mean value right after the exam. After all those nasty questions, am I gonna lose tons of marks on this one?😭😭😭

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