Run the simulation using n = 30 and N = 10 for a uniform, a bell-shaped, and a skewed distribution.
§ Identify the mean of the sampling distribution of sample means for each distribution.
§ Evaluate if the results are what you expected for each distribution.
Run the simulation again using n = 30 and N = 1000 for a skewed distribution.
§ Describe the shape of the distribution of sample means.
Inadequate or unclear data.
What are you running the simulation on?
If n = number of scores, what is N?
Will the skew be positive (tail to the right) or negative (tail to the left)?
N = 6
To run the simulation, you will need a dataset that follows each of the described distributions: uniform, bell-shaped, and skewed. Additionally, you'll need to specify the sample size (n) and the number of samples (N) to use in the simulation.
Once you have the dataset and the required parameters, you can follow these steps to obtain the mean of the sampling distribution of sample means:
1. For each distribution, randomly select n observations from the dataset to form a sample.
2. Calculate the sample mean for each sample.
3. Repeat steps 1 and 2 N times to obtain N sample means.
4. Calculate the mean of these N sample means.
By following these steps, you will determine the mean of the sampling distribution of sample means for each distribution.
To evaluate if the results are what you expected for each distribution, compare the mean of the sampling distribution of sample means to the population mean of the original dataset. If the means are similar or close to each other, the results align with your expectations. However, if the means are significantly different, it may indicate that your simulation did not accurately capture the characteristics of the distribution.
For the second part of the question, you are asked to describe the shape of the distribution of sample means when running the simulation with n = 30 and N = 1000 for a skewed distribution. To answer this, you need to perform the simulation with these parameters, as well as choose a skewed distribution for your dataset.
After obtaining the sample means, plot a histogram or a density plot of these means. This plot will show the distribution of the sample means. Analyze the shape of the distribution visually and describe it accordingly. It is likely to observe that the shape of the distribution of sample means approaches a normal or bell-shaped distribution, even if the original dataset had a skewed distribution. This phenomenon is called the central limit theorem and is a fundamental concept in statistics.