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### Sampling Distributions

Course: MATH 1710, Fall 2007
School: Cornell
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Word Count: 520

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Lawless Section Megan 3 CASE 1 1. In ticks.1, 4 ticks carry the disease. That's 4/20 or 20% of the ticks. It is unlikely that a sample of only 20 ticks would have the same frequency of the disease as the entire population of 10000 ticks. The shape of this histogram is not well defined, since the range of values is so small. It is somewhat skewed to the left. The mean would seem to be between 0.1 and 0.15. This...

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Lawless Section Megan 3 CASE 1 1. In ticks.1, 4 ticks carry the disease. That's 4/20 or 20% of the ticks. It is unlikely that a sample of only 20 ticks would have the same frequency of the disease as the entire population of 10000 ticks. The shape of this histogram is not well defined, since the range of values is so small. It is somewhat skewed to the left. The mean would seem to be between 0.1 and 0.15. This indicates that, when a sample of 20 ticks is taken, there are usually between 10% and 15% carrying the disease, although the values range from 0 to 20%. 2. 3. Megan Lawless Section 3 4. The shape of the graph becomes more symmetric as larger samples are used. The mean becomes easier to see with more samples. The range of values decreases as the number of samples taken increases. We began with values ranging from 0 to 20%, but the last graph had a range of 8% to 12% of ticks carrying the disease. The level of tick infestation in the entire population is probably well represented by the graph created using sample sizes of 1000 ticks. CASE 2 1. The shape is somewhat symmetric, but clearly skewed to the right. The mean is somewhere around \$10,000. Costs range from near 0 to \$50,000. There were 12,145 patients. The mean cost for their treatment was \$9,879. 2. The sample size n=24. The mean of this sample is \$10,737. Some other means of samples were \$9,948; \$10,109; and \$9,867. Some of these samples are more accurate than others. Some are off by several hundred dollars. 3. The graph is fairly symmetrical. The mean is \$10,000. around The values range from around \$8,000 to \$12,000. Megan Lawless Section 3 4. A larger sample would help mostly by showing the variety of costs for patients. Although the mean in our samples was roughly the same as that of the entire group, the spread was much smaller. It did not reflect the great range of costs that we see in the entire sample. Looking at the graph, we see that the range has decreased from our previous \$8000-\$12000 to \$8000-10500. So increasing the sample obviously did not increase the range, but it did give us a mean very close to the mean of the entire set of data. This graph still looks quite different from the graph of the entire population, but we still can get useful data from it. 5. Although this graph still does not resemble the graph of the entire data set, it gives us a mean within \$.02 of the actual mean. This would be more than accurate enough if someone were trying to find the mean cost of treatment for heart attack patients using only a sample. It turns out that a large range is unnecessary to find an accurate mean. 6. A larger sample size will always increase the accuracy of the information. The center of a sample becomes more representative of the true center as sample size increases, although often a very large sample is not needed to obtain a general estimate of the mean. The shape of the sample graphs will more closely resemble the graph of the entire set of data as the sample size increases. The spread of data using samples becomes smaller as the sample size increases.
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