sampling distrubutions assignment

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Wilmington University *

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308

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Mathematics

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Apr 3, 2024

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docx

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MAT308 Name:________________________ Investigation Sampling Distributions of Objectives In this activity, you will use the applet for investigating the sampling distribution of . You will use the applet to explore the shape of the sampling distribution when the population is normally distributed and when the population is not normal. Materials Computer with internet access – one per student or pair of students. Launch the Sampling Distributions applet at http://onlinestatbook.com/stat_sim/sampling_dist/index.html . When the BEGIN button appears on the left side of the screen, click on it. You will see a yellow page entitled “Sampling Distributions”. 1. There are choices for the population distribution: Normal, uniform, skewed, and custom. The default is Normal. Click the “Animated” button. ● What happens? When the animated button is pushed, some of the black boxes drop below to create the sample data graph and a blue box drops below into the distribution of means data graph. ● Click the button several more times. What do the black boxes represent? The black boxes represent people drawn from the population at random to create a sample set. ● What is the blue square that drops down onto the plot below? The blue square is the sample mean that comes from the samples drawn from the population. ● What does the red horizontal band under the population histogram tell us? The red horizontal band tell us the standard deviation based around the sample mean. Majority of the sample cases lie around that red band.
Notice the left panel. Important numbers are displayed there. Did you notice that the colors of the numbers match up with the objects to the right? As you make things happen, the numbers change accordingly, like an automatic scorekeeper. 2. Click on “Clear lower 3” to start clean. Then click on the “10,000” button one time under “Sample;” to simulate taking 10,000 SRSs of size n = 5 from the population. Answer these questions: ● Does the approximate sampling distribution (blue bars) have a recognizable shape? Click the box next to “Fit normal.” The approximate sampling distribution shows a normal bell-shaped distribution, which is a shape we have talked about previously in class. ● Compare the mean of the approximate sampling distribution with the mean of the population. The mean of the sampling distribution and the mean of the population seem to be equal at 16. ● How is the standard deviation of the approximate sampling distribution related to the standard deviation of the population? The standard deviation of the approximate sampling distribution is a little under half of the standard deviation of the population, with the sampling standard deviation being 2.23 and the population standard deviation being 5. 3. Use the drop-down menus to set up the bottom graph to display the mean for samples for size n = 20. Then sample 10,000 times. How do the two distributions of compare: shape, center, spread? The two distributions share the same characteristics. Both samples have the same bell-shaped shape and are in the center of the spread. The sample at the size n=5 has more variability than the sample at size n=20. 4. What have you learned about the shape of the sampling distribution of when the population has a Normal shape? Because the two distributions seem to mirror each other, when the population has a normal shape, the sample distribution will also be normal. 5. Now select “Skewed population. Set the bottom two graphs to display the mean---one for samples of size 2 and the other for samples of size 5. Click the Animated button a few times to be sure you see what’s happening. Then “Clear lower 3” and take 10,000 SRSs. Describe what you see. A larger sample size of n=5 has less spread of its standard deviation compared to the sample size n=3. 6. Change the sample sizes to n = 10 and n = 16 and repeat Step 1. What do you notice? A larger sample size of n=16 has less spread of its standard deviation compared to the sample size n=10.
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