Question.2925 - For this discussion board, please complete the following steps: https://www.youtube.com/watch?v=4YLtvNeRIrg Go to: http://onlinestatbook.com/stat_sim/sampling_dist/Links to an external site. (It is helpful to have the applet and the exercise instructions side-by-side in two separate windows.) Click on the “Instructions” link to become familiar with how the applet works Complete the following two Applet Exercises: Applet Exercises: Task 1: Start with a normally shaped distribution for your population. Set the sample size to 5. Obtain 10,000 random samples of size n=5. Describe the distribution of the sample mean based on the results of the applet. That is, describe the shape, center (mean), and spread (standard deviation) of the distribution. 2. Set the sample size to 10. Obtain 10,000 random samples of size n=10. Describe the distribution of the sample mean based on the results of the applet. 3. Set the sample size to 30. Obtain 10,000 random samples of size n=30. Describe the distribution of the sample mean based on the results of the applet. 4. What happens to the sampling distribution of the mean as the sample size increases? Be sure to answer with complete sentences. Task 2: Create your own distribution for your population by changing the drop down menu to the right to “Custom”. Set the sample size to 5. Obtain 10,000 random samples of size n=5. Describe the distribution of the sample mean based on the results of the applet. That is, describe the shape, center (mean), and spread (standard deviation) of the distribution. 2. Set the sample size to 10. Obtain 10,000 random samples of size n=10. Describe the distribution of the sample mean based on the results of the applet. 3. Set the sample size to 30. Obtain 10,000 random samples of size n=30. Describe the distribution of the sample mean based on the results of the applet. 4. The Central Limit Theorem states that the sampling distribution of the mean approaches a normal distribution as the sample size increases. Sample from your distribution and determine how large a sample size is needed for the distribution to be a very close approximation of the normal distribution. Please include a screenshot (like the one below) of the applet that includes your own distribution and the sampling distributions when obtaining 10,000 samples. This can either be done by attaching or embedding the image using the “Image icon”Links to an external site..
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Task 1The shape is symmetric and normally distributed, with a mean of 15.96 and a Standard deviation of 2.25 The shape is symmetric and normally distributed, with a mean of 16.00 and a standard deviation of 1.58 The shape is symmetric and normally distributed, with a mean of 16.01 and a standard deviation of 1.00 (Sampling Distributions (7.2), n.d.) As the sample size increases, the sampling distribution of the mean decreases. Task 2 The shape is symmetric and normally distributed, with a mean of 17.41 and a Standard deviation of 3.18 The shape is symmetric and normally distributed, with a mean of 17.39 and a standard deviation of 2.24 The shape is symmetric and normally distributed, with a mean of 17.40 and a standard deviation of 1.41(2.1 Sampling Distribution of Means, n.d.) If N is greater than and equal to 30, the sampling distribution of the mean approaches a normal distribution. References 2.1 Sampling Distribution of Means. (n.d.). Www.uth.tmc.edu. https://www.uth.tmc.edu/uth_orgs/educ_dev/oser/L2_1.HTM#:~:text=As%20the%20sample%20size%20increases%20the%20standard%20deviation%20of%20the Sampling Distributions (7.2). (n.d.). Www.youtube.com. Retrieved October 21, 2023, from https://www.youtube.com/watch?v=7S7j75d3GM4 ? ?More Articles From Statistics
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