Best Way To tell The Difference from T&Z for Hypothesis Testing?

This confuses me quite a bit. What are certain words I need to look for to know. I know the rule with if the STD is known or not... Sometimes it's given to me in S and the other in the STD symbol. But can I get some help on a way to really tell the difference, please?

Re: Best Way To tell The Difference from T&Z for Hypothesis Testing?

Usually S^2 is the sample variance (variance estimated from a sample) and SD refers to a population standard deviation.

You will need to read each source carefully to know exactly what is what though in general.

Re: Best Way To tell The Difference from T&Z for Hypothesis Testing?

Quote:

Originally Posted by

**chiro** Usually S^2 is the sample variance (variance estimated from a sample) and SD refers to a population standard deviation.

You will need to read each source carefully to know exactly what is what though in general.

But let me give you a better example of both.

A psychologist obtains a random sample of 20 mothers in the first trimester of their pregnancy. the mothers are asked to play Mozart in the house at least 30 minutes each day until they give birth. After 5 years, the child is administred an IQ test. We know that IQ's are normally distribute with a mean of 100 and STD of 15. If the IQ's of the 20 children in the study result in a sample mean of 104.2 is there evidence that the children have higher IQ's? Use the (alpha symbol) =.05 level of significance.

In 2001, the mean contract interest rate for a conventional 30 year first loan for the purchase of a single home was 6.3%, according to the US federal Housing Board. A real estate agent believes that interest rates lower today and obains a random sample of 41 recent 30 year convetional loans. The mean interest rate was found to be 6.05% with a STD of 1.75 percent. Is this enough evidence at the the alpha=.05 level of significance?

First one you will use, Z, the second one T. So I am wondering how do you really tell the difference?

Another example, I got wrong on a previous exam because I took the wrong one.

Stacie Statistic is doing her BSP on the time that -full time local student spend on HW perweek. Her group has a random sample of 40 full time students with a mean 32 hours and STD of 8 hours.

I picked Z for this but it was suppose to be T.

Re: Best Way To tell The Difference from T&Z for Hypothesis Testing?

If you are talking about underlying distributions then you just need to know what kind of test statistic you are using.

The T distribution typically uses the sample mean and sample variance while a lot of results for using Z are based on the Central Limit Theorem and the Asymptotic results like the Wald Statistic and others.

If you know what kind of information you are using and the nature of the test statistic, you will know whether its a t-distribution or a Normal distribution.

Re: Best Way To tell The Difference from T&Z for Hypothesis Testing?

Quote:

Originally Posted by

**chiro** If you are talking about underlying distributions then you just need to know what kind of test statistic you are using.

The T distribution typically uses the sample mean and sample variance while a lot of results for using Z are based on the Central Limit Theorem and the Asymptotic results like the Wald Statistic and others.

If you know what kind of information you are using and the nature of the test statistic, you will know whether its a t-distribution or a Normal distribution.

Thank you for replying btw. I have 1 more question.

Another example(If you do not mind), I got wrong on a previous exam because I took the wrong one.

Stacie Statistic is doing her BSP on the time that -full time local student spend on HW perweek. Her group has a random sample of 40 full time students with a mean 32 hours and STD of 8 hours.

I picked Z for this but it was suppose to be T. I am wondering why was this suppose to be T instead of Z?

Each chapter it tells me which one I am going to be using but when it comes to the exam both the questions sounds the same and I get them mixed up.

Re: Best Way To tell The Difference from T&Z for Hypothesis Testing?

The key word here is "sample". Your mean and standard deviation are sample estimates, not population estimates.

Re: Best Way To tell The Difference from T&Z for Hypothesis Testing?

Yeah, I am really sorry. Wen I look at some of the other questions, they are essentially written the same but yet one is Z the other T(like the ones above). Yeah, I am just trying to go back and re-reading the difference from population and sample.

Re: Best Way To tell The Difference from T&Z for Hypothesis Testing?

Quote:

Originally Posted by

**chiro** The key word here is "sample". Your mean and standard deviation are sample estimates, not population estimates.

Just one thing(kind of going senile here looking at my book and computer for the longest) what do you mean by sample estimates and not population estimates?

Re: Best Way To tell The Difference from T&Z for Hypothesis Testing?

Sample means that you have a sample drawn from a population. Typically populations are infinite (or really large) and samples are just a small representation of tha ist population.

If you collect data, then it is typically a sample. The only time when it is considered a population would be if it was say a national census or something similar. Otherwise its a sample.

Sample estimates are point estimates of population parameters using the sample. This is the case if the estimator is unbiased. If its biased, you correct it to make it unbiased.

The sample variance estimates the population variance and the sample mean estimates the population mean. Estimators are random variables so they have a distribution and variance.