Paired or unpaired? In each of the following settings,...

Paired or unpaired? In each of the following settings, decide whether you should use paired $t$ procedures or two-sample $t$ procedures to perform inference. Explain your choice. ${ }^{40}$ (a) To compare the average weight gain of pigs fed two different rations, nine pairs of pigs were used. The pigs in each pair were littermates. A coin toss was used to decide which pig in each pair got Ration $\mathrm{A}$ and which got Ration $\mathrm{B}$. (b) Separate random samples of male and female college professors are taken. We wish to compare the average salaries of male and female teachers. (c) To test the effects of a new fertilizer, 100 plots are treated with the new fertilizer, and 100 plots are treated with another fertilizer. A computer's random number generator is used to determine which plots get which fertilizer.

Paired or unpaired? In each of the following settings, decide whether you should use paired $t$ procedures or two-sample $t$ procedures to perform inference. Explain your choice. ${ }^{40}$
(a) To compare the average weight gain of pigs fed two different rations, nine pairs of pigs were used. The pigs in each pair were littermates. A coin toss was used to decide which pig in each pair got Ration $\mathrm{A}$ and which got Ration $\mathrm{B}$.
(b) Separate random samples of male and female college professors are taken. We wish to compare the average salaries of male and female teachers.
(c) To test the effects of a new fertilizer, 100 plots are treated with the new fertilizer, and 100 plots are treated with another fertilizer. A computer's random number generator is used to determine which plots get which fertilizer.

Key Concepts

Dependent versus Independent Measurements

Understanding whether measurements are dependent or independent is crucial in selecting the appropriate t-test. Dependent measurements, as seen in matched pairs or repeated measurements on the same subjects, benefit from paired t-test procedures that account for within-pair correlations. In contrast, independent measurements require methods like the two-sample t-test that assume no relationship between the observations of the two groups.

Paired t-test

The paired t-test is used when the data sets are not independent but are collected in pairs such that each observation in one sample has a unique, corresponding observation in the other sample. This design is particularly beneficial when the paired observations are naturally linked, such as measurements before and after treatment on the same subjects or in matched experimental units, because it helps control for variability between pairs.

Two-sample t-test

The two-sample t-test is used when comparing the means of two independent groups, where the observations in one group have no inherent link to observations in the other group. This test assumes that the two groups are randomly sampled from populations that potentially have different means, and it is ideal for cases when no pairing or matching of experimental units exists.

Transcript

00:01 In this video we are focused on finding out that for which of the settings we should use paired t procedures and for which one we should use two sample t procedures to perform inference.

00:12 So here we can write that if every value and it will be here that in one sample basically we are talking about if every value in one sample is having a corresponding value and it will be here like this.

00:29 That is corresponding and then here it is going to have the word while value and this is we are talking about the other sample so it can be written over here like this so if it happens then we should use paired t procedures so it can be written use paired t procedures hence it can be written over here as p -r -o -c -e -d -u -u - res.

01:01 Now we can say else use two sample t procedures.

01:06 So it will be to sample sample and then here it is going to be t procedures.

01:13 So from this very information if we look into the options that is first option then here it can be said that in the first option we must use paired t procedures because each subject has a litter in other sample.

01:31 So, it can be written over here like this.

01:35 And this will be the answer for the first part of this very problem.

01:40 Now, here we can talk about the second part.

01:43 And in the second part, we can write that we must use the two sample t proportions and it will be here to sample the procedures, not proportion, it will be procedures.

01:59 Very sorry for saying it wrong...

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