# Paired difference T-Test

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• August 7th 2011, 02:36 AM
thomasboateng
Paired difference T-Test
The operators think that machine B tends to deliver a somewhat greater amount than machine A, no matter what the ambient temperature. This is being investigated by an experiment. A random sample of 10 results from the experiment is shown below. Each column of data is for a different ambient temperature

Use an appropriate t test to examine, at the 5% level of significance, whether the mean amount
delivered by machine B may be taken as being greater than that delivered by machine A,
stating carefully your null and alternative hypotheses and the required distributional
assumption.

this is the table

Amount
delivered by 246.2 251.6 252.0 246.6 258.4 251.0 247.5 247.1 248.1 253.4
machine A
Amount
delivered by 248.3 252.6 252.8 247.2 258.8 250.0 247.2 247.9 249.0 254.5

the difference mean is 0.64

but what i don't understand is how they get for the standard deviation s(n-1)=0.8316
• August 7th 2011, 01:57 PM
pickslides
Re: Paired difference T-Test
Quote:

Originally Posted by thomasboateng

but what i don't understand is how they get for the standard deviation s(n-1)=0.8316

I don't know what this figure is, each machine will have its own variance and because this is a paried test there will be a pooled variance to help caclulate the test statistic.

$\displaystyle H_0: \mu_B \leq \mu_A \implies \mu_B - \mu_A\leq 0$

so $\displaystyle H_A: \mu_B > \mu_A \implies \mu_B - \mu_A > 0$

After doing this test I found a p-value of 0.71, what does this mean?
• August 8th 2011, 04:55 AM
thomasboateng
Re: Paired difference T-Test
I understand how to get the critical value its 1.833 but i don't get how you get the p value or the standard deviation?
• August 8th 2011, 05:00 AM
CaptainBlack
Re: Paired difference T-Test
Quote:

Originally Posted by thomasboateng
I understand how to get the critical value its 1.833 but i don't get how you get the p value or the standard deviation?

If you have the critical value you do not need the p-value, what you do need is the value of the test statistic, which you will compare with the critical value.

CB
• August 8th 2011, 06:47 AM
thomasboateng
Re: Paired difference T-Test
i see. the formula for the test statistic is easy enough except for i dont get which steps they used in order to obtain the standard deviation
• August 8th 2011, 07:23 AM
matheagle
Re: Paired difference T-Test
question 1) explain 'greater amount' of what
question 2) why is this a paired t-test?
Is it just because the two samples sizes are the same?
That necessary, not sufficient.
• August 8th 2011, 10:13 AM
thomasboateng
Re: Paired difference T-Test
why wouldnt it be. it has the characteristics for a paired diff test. it doesnt matter what it produces thats not the point
• August 8th 2011, 12:04 PM
matheagle
Re: Paired difference T-Test
If the two samples are independent then it's not a paired difference experiment.
I do not see enough information go either way.
• August 8th 2011, 01:43 PM
CaptainBlack
Re: Paired difference T-Test
Quote:

Originally Posted by matheagle
If the two samples are independent then it's not a paired difference experiment.
I do not see enough information go either way.

The machines are at a common temperature which varies from sample period to sample period. The null hypothesis is that the difference between the machine outputs in a period has zero mean. A paired test is appropriate (subject to the other conditions for a t-test being applicable).

CB
• August 8th 2011, 03:45 PM
thomasboateng
Re: Paired difference T-Test
yeah i know that. but standard deviation method?
• August 8th 2011, 08:52 PM
CaptainBlack
Re: Paired difference T-Test
Quote:

Originally Posted by thomasboateng
yeah i know that. but standard deviation method?

The SD of the differences s_D is computed in the usual way (there is just one sample of differences). Use the population SD estimate formula (that is the one with division by n-1 rather than n). The standard error is required for the test is s_D/sqrt(n) where n is the number of differences.

CB
• August 8th 2011, 09:18 PM
matheagle
Re: Paired difference T-Test
when you take the differences
this just becomes a one sample test.
t is appropriate when the population of differences is normally distributed
and you don't have the population variance from the population of all differences
• August 9th 2011, 09:58 AM
thomasboateng
Re: Paired difference T-Test
and what is this usual way?
• August 9th 2011, 10:02 AM
CaptainBlack
Re: Paired difference T-Test
Quote:

Originally Posted by thomasboateng
and what is this usual way?

What is the formula for computing the SD form a sample?

CB
• August 9th 2011, 11:23 AM
thomasboateng
Re: Paired difference T-Test
yes this is my question what is the forumula for standard deviation.
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