significance level

[hopetobeat]

For a hypo test with a prob of a Type 2 error of 60% and a probability of a Type 1 error of 5%, which of the following statement is most accurate?

A. The power of the test is 40%, and there is a 5% probability that the test statistic will exceed the critical value.

B. There is a 95% probability that the test statistic will be between the critical values if this is a two-tail test.

C. The power of test is 55%, and the confidence level is 95%.

D. There is a 5% probability that the null hypo will be rejected when actually true, and the probability of rejecting the null when it is false is 40%.


D is absolutely right.
I am quite confused about relation between significant level and confidence interval. Can I say significant level of 5% means confidence interval of 95% as in choice C? And how about B?
Thanks.

 

[Dreary]

D is right.

Significance level is alpha (5%) The power of the test is 1-alpha (95%)
Confidence level? I'm not sure.

If this was a two-tail test, then you have 2.5% on each side, and so you will have 95% probability of the calculated t being within the critical values. So B sounds good, unless they don't mean calculated test when they say "test statistic".

 

[strangedays]

hopetobeat,
it is not 100% right I mean,

Consider the following confidence interval: We are 90% confident that the population mean is greater than 100 and less than 200.

Usually, we assume that this means that there is 90% chance that the population mean falls between 100 and 200. This is incorrect. Like any population parameter, the population mean is a constant, not a random variable. It does not change. The probability that a constant falls within any given range is always 0.00 or 1.00.

The confidence level describes the uncertainty associated with a sampling method. Suppose we used the same sampling method to select different samples and to compute a different interval estimate for each sample. Some interval estimates would include the true population parameter and some would not. A 90% confidence level means that we would expect 90% of the interval estimates to include the population parameter.

 

[Milos]

Significance level is alpha (5%)
Confidence level is 1-alpha (95%)
The power of the test is 1-Type II error (40%)

Milos



Edited 1 time(s). Last edit at Friday, May 16, 2008 at 11:50AM by Milos.

 

[hopetobeat]

Dreary Wrote:
-------------------------------------------------------
> D is right.
>
> Significance level is alpha (5%) The power of the
> test is 1-alpha (95%)
> Confidence level? I'm not sure.
>
> If this was a two-tail test, then you have 2.5% on
> each side, and so you will have 95% probability of
> the calculated t being within the critical values.
> So B sounds good, unless they don't mean
> calculated test when they say "test statistic".

Dreary
Power of test is 1- probability of type 2 test, not type 1. Sig-level = probability of type 1 test

 

[hopetobeat]

strangedays Wrote:
-------------------------------------------------------
> hopetobeat,
> it is not 100% right I mean,
>
> Consider the following confidence interval: We are
> 90% confident that the population mean is greater
> than 100 and less than 200.
>
> Usually, we assume that this means that there is
> 90% chance that the population mean falls between
> 100 and 200. This is incorrect. Like any
> population parameter, the population mean is a
> constant, not a random variable. It does not
> change. The probability that a constant falls
> within any given range is always 0.00 or 1.00.
>
> The confidence level describes the uncertainty
> associated with a sampling method. Suppose we used
> the same sampling method to select different
> samples and to compute a different interval
> estimate for each sample. Some interval estimates
> would include the true population parameter and
> some would not. A 90% confidence level means that
> we would expect 90% of the interval estimates to
> include the population parameter.


strangedays, so can you explain why B is wrong? Thanks.

 

[strangedays]

B. There is a 95% probability that the test statistic will be between the critical values if this is a two-tail test.

while:
A 95% confidence level means that we would expect 95% of the interval estimates to
include the population parameter.

Can you see the difference? in B it says "critical values" which is used to reject or not the null hypotesis.

while 95% is the interval we test if the population parameter lie within the confidence level.

 

[strangedays]

Anyway...I am going for a pint now it is friday..and I need two hour break as my brain is frying!.

I will follow up later!!! I love this forum...you guys are all cool!!!!!!!!!

 

[Dreary]

Thanks all for the corrections.