# Use T-Statistic? Or use the Z value?

• April 4th 2008, 04:52 PM
darren_a1
Use T-Statistic? Or use the Z value?
1. The local Tupperware dealers earned these commissions last month:

$4377.47$3183.76 $1970.16$2270.88 $3860.06$2508.55 $1569.64$4205.30 $1663.68$3960.71

Assuming the population for the amount of commissions earned by Tupperware dealers last month is known to be normally distributed, create a 95% confidence interval estimate for , the mean amount of commission earned.

You will be asked to identify x-bar, s, alpha, df, t, E and the confidence interval.

My main Q here would be whether I would use Z statistic or I should use the T-statistic? also any idea on how to compute df?

Cheers

Darren
• April 4th 2008, 07:27 PM
mr fantastic
Quote:

Originally Posted by darren_a1
1. The local Tupperware dealers earned these commissions last month:

$4377.47$3183.76 $1970.16$2270.88 $3860.06$2508.55 $1569.64$4205.30 $1663.68$3960.71

Assuming the population for the amount of commissions earned by Tupperware dealers last month is known to be normally distributed, create a 95% confidence interval estimate for , the mean amount of commission earned.

You will be asked to identify x-bar, s, alpha, df, t, E and the confidence interval.

My main Q here would be whether I would use Z statistic or I should use the T-statistic? also any idea on how to compute df?

Cheers

Darren

First question to ask: Do you know the population standard deviation? No?

Second questions to ask: Is the value of n 50 or more (some folk are less conservative and use 30 or so)? No?

Then you use the t-statistic with df = n-1 where n is the sample size. You should know these things!
• April 4th 2008, 07:52 PM
falcald
Darren,
The T-Test is robust under non-Normal distributions. Even when you do not know that distribution. In the case you describe, T-Test should be used because you have just a sample and the population is Normally distributed... but the test can be applied only if you have more than 30 observations (many authors use more than 35... ). Whatever, you have 10.
If this is a textbook example (and we can ommit the detail that I explained above), I would use T-Test because you do not know the population variance and the population is Normally distributed.
Hope this helps.

Federico.
• April 5th 2008, 08:58 PM
mathceleb
Quote:

Originally Posted by darren_a1
1. The local Tupperware dealers earned these commissions last month:

$4377.47$3183.76 $1970.16$2270.88 $3860.06$2508.55 $1569.64$4205.30 $1663.68$3960.71

Assuming the population for the amount of commissions earned by Tupperware dealers last month is known to be normally distributed, create a 95% confidence interval estimate for , the mean amount of commission earned.

You will be asked to identify x-bar, s, alpha, df, t, E and the confidence interval.

My main Q here would be whether I would use Z statistic or I should use the T-statistic? also any idea on how to compute df?

Cheers

Darren

Darren,

From you sample population, I calculate $\overline{x} = 2957.021$ and $\sigma = 1034.0950$. I got that from here: Mean, Variance, and Standard Deviation

You had asked about how to calculate the t-statistic. I built this for you tonight. For the answer to your problem, I get: $2217.2600 < \mu < 3696.7820$

Go here: Student t-Test Confidence Interval for Mean

We know n = 10, and you want a 95% confidence interval for the mean. Enter those values and take a look at the answer and the math work involved. This will show you how to do this in the future. I built a note in the math for how to calculate the t-score value based on $\alpha$ using Excel's TINV function.

For future reference, this lesson is located on the statistics menu and is searchable by confidence, interval, student-t, mean.

Let me know if you have questions.
• April 6th 2008, 05:35 AM
CaptainBlack
Quote:

Originally Posted by falcald
Darren,
... but the test can be applied only if you have more than 30 observations (many authors use more than 35... ).

Student's t-test is a small sample test for normally distributed data with unknown variance. If we has a known variance then a z-test would be appropriate, similarly if we have a large sample size.

If we had a sample size were 30 or more we would be tempted to use a z-test (though I would hold out for a sample size of 100 myself).

RonL