Question

I need to develop a research question and determine how I would organize the study to use random sampling.I need to show all my work. Can you please help?

Answer 1

Random sampling is a technique that is applied to create a sample in which every sample of the population has the equal chance of being selected. Here, from the population sample elements are selected randomly without any bias.

Example...

Suppose there is a school with 1000 teachers. The principal of the school is approached by two training agencies with their respective training modules and out of these only one is to be selected. But the point is that, the principal is in confusion as she doesn't know which one to select among them as both the programs are new to the school. It is essential for the school to conduct a training program in order to improve the productivity of its students. These training modules teaches the teachers how to teach the students in order to improve the academic metrics of the school.

In this regard, the teacher made three different sample of 11 members each. One of these sample will not be given any training and the other two will be allotted to both the training programs. In this regard, say there are 3 groups of teachers i.e. A, B and C... A will not be given any training and B will be allotted to the first agency and C t to the other agency.

While selecting the members of each sample, a random sampling technique will be used. Here out of the 1000 teachers 33 teachers will be selected randomly without any bias such that every teacher has the equal probability of being selected.

Again, from the selected 33 teachers, each of them will be attached to any of the three groups A, B and C randomly such that there are 11 members in each sample.

The research question is that: "Which among the two training programs is more effective for the Teachers"

Here, after the training is over a rating will be given to each of the members on the basis of a questionnaire. These questions might be a psychometric test or so. The final aim of the experiment will be:

1. Whether the two training models are really effective. It can be analysed by analyzing the mean ratings of the samples in the Group B and C to that of A.

2. If yes, then which among the two is the best.

A sample output is shown below as an example for reference purpose...

Sample rating for the taste score (on a scale of 1-10).

Take one group as a dependent and the other two as an independent variable in this experiment. A One Factor Anova will be performed in this regard to derive the output...

Kindly note that this is a sample output where we are comparing the data of three different groups.

Here, you can see that the P value is 1.75 * 10^-7

If we take the confidence level as 95% (Alpha will 0.05)

Then,

Alpha = 1 - Confidence Level

= 1 - 0.95

= 0.05

Alpha level is the probability of rejecting the null hypothesis when the null hypothesis is true.

Hypothesis:

H₀: U₁ = U₂ = U₃ (Null Hypothesis)

H_a: All the means are not equal (Alternate Hypothesis)

Where,

U is the mean rating of the respective groups.

Here as the P value is smaller than 0.05, so we can state that the null hypothesis is not accepted. This is because there occurs a significant difference in the means of all the three groups.

Similarly for your case, if there is a such significant difference, then you can state that the three groups doesn't have the same ratings on an average.

After this we can do a post hoc test to compare the three groups. This will help us to come to a final conclusion of selecting a particular training module...

End of the Solution...