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# Conditions for valid t intervals

Examples showing how to determine if the conditions have been met for making a t interval to estimate a mean.

## Want to join the conversation?

• Why can't we use the '# of Success & #of Failure both >/= 10' test to test for Normality?
• I think it is because in this case we are not going to calssify people's age as success or failure.
If we want to know the number of faculty members that older than 30 years old, then we may classify success (older than 30 yrs) and failure (not older than 30 yrs).
• @ previously in the videos of central limit theorem it was said that as your sample size approach infinity the sample distribution of the sample mean approaches normal. and said it is not that extent "approach infinity" 10 or 20 samples are enough to approach normal dist of sample mean.
NOW WHERE THIS 30 SAMPLE RULE CAME FROM?
• If you want the sample mean distribution approaches normal with 10 or 20 samples then the size of each samples must >= 30 (30 is the size of a sample not 30 samples).
If your sample's size is < 30 and if the distribution of the population is not normal (in this video the population distribution is right skew) then then sample mean distribution won't approach normal even the number of samples you make approach infinity.
• Regarding the second assumption (normality), isn't it rather law of large number than central limit theorem that would ensure that? After all, we only have one random sample.
• The law of large numbers tells us only that the sample mean will converge to the population mean without telling us how it is distributed which is necessary when we are talking about confidence intervals.
• @ said that we use t* and when we don't have access to the sample standard deviation of the sample distribution we use the sample standard deviation.
didn't he mean to say that when we don't have access to the (( true population standard deviation .............. )) ? as sample distribution is a part of building our estimation and we use the known parameters "if any, like pop S.D" but often we don't know such parameter then we use the sample S.D
is that true? we use sample S.D instead of the missing parameter not instead of the missing s.D of sample distribution.
• I am having some trouble understanding your question exactly. You seem to be asking why we don't know the population parameters (mean and standard deviation). I will try to explain what I think.
In general we are using a sample to estimate the parameters of a population because it is impractical to know something about every item in a true (often large) population. For example, it is too expensive for a child seat company to call all parents about their opinions on a new carseat design. So we take a sample, a subset of the total population.
The standard deviation of the sampling distribution is the standard error, which is approximated by the standard deviation of our sample (it cannot be by the standard deviation of the population because we do not know that parameter) divided by the square root of our sample size. We don't know the 'true' standard deviation of a sampling distribution.
(1 vote)
• I asked same question for later video about "z - statistics vs t - statistics"

At , the one of conditions for t - testing is met when sample size, n, is greater or equal to 30.

However, the later video (which I mentioned on first line of sentence) says that we should use T- statistics when we have less than 30 for our sample size.

Could you please clarify this for me?

Thanks!
• Ok basically the conditions for Z and T include
1. SRS
2. Normality (n>30)
3. Independence
ALL conditions must be met to use Z. For T, though it is preferred to meet all the conditions, the test is possible to use with 1 or more of the conditions violated.
• Couldn't you just say that the sampling distribution is approximately normal if:

(1) sample size >= 30
(2) the population distribution is roughly symmetric

The population distribution being normal itself would satisfy the second condition, so it seems like it doesn't actually add anything.
• I read from other sources that we use t statistics when n<= 30. Why Sal is saying the opposite here?