Picturing things in the plane has been a bugaboo (I've been dying to use that word) for a long time. The prof I had for my first measure theory class told this story for us to chew on.
A physics professor, an engineering professor, and a mathematics professor had all died. They were being...
The words "standardized" and "normalized" get tossed around quite a bit in these discussions, rather like "derivative" and "integral" get tossed around in analysis: the words can mean different procedures while describing things that are quite similar in concept.
Think about the correlation...
The chi-square test can only indicate whether there is or is not an association.
I'm not sure how finding out that a greater percentage of women are left-handed than right-handed would give any information about women being more left-handed than men. Can you expand on how you reached that...
When would you use chi-square to test equality of means? I don't know of such a case.
If you're doing a chi-square test for independence there is no "one-sided" vs "two-sided" situation to consider.
If you're doing a chi-square test to test equality of proportions the alternative is always two...
The comments below are good, but there is one more thing that needs to be pointed out: you CANNOT say things like
"more than 50% of the girls scored higher than Cindy."
based on the information here: that assumes the the test scores are symmetric (the horribly named "normally distributed") so...
"Afterward, you can see that the t-statistic T is a ratio of a normal random variable with a chi random variable."
An important word is missing: independent. The sample mean and sample standard deviation have to be independent in order for the statistic T to have a t-distribution. Assuming the...
we say that the sample mean converges in probability to the population mean: that is, given n epsilon, it is true that the limit as n goes to infinity of P(|Xbar - mu| > epsilon) = 0 (or, equivalently, the limit of
P(|Xbar - mu| <= epsilon) = 1).
It's only when the sequence is standardized...
Not very useful, and the greater the skewness the less useful the standard deviation and the mean are. Once you get away from the textbook ideal of data being normally distributed you should also get away from using the mean and standard deviation, as both are impacted by the skewness.
You have (IMO) the wrong calculation. If the claimed accuracy is 95%, but you suspect
a) that it is less than 95%, based on your observed data the calculation should be to find the probability of getting AT MOST 93 correct out of 100 tries. You have the probability that the success rate is...
Imagine you want to test H0: mu = 98.6F versus Ha: mu < 98.6F
where the quantity we're concerned with is body temp of a "normal healthy" adult.
Concerning your "neither true nor false" question, think about it this way: are we trying to say that the mean temperature is EXACTLY 98.6 degrees F...
"A type II error would mean (the null hypothesis) is false"
No, it doesn't. Just as we never talk about "accepting" either hypothesis, remember that
- rejecting the null does not prove the null value is false, and does not show the alternative value is true
- failing to reject the null, does...