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.
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”.
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.
Significance level is alpha (5%) Confidence level is 1-alpha (95%) The power of the test is 1-Type II error (40%) Milos
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
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.
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.
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!!!
Thanks all for the corrections.