This course was intended to provide a basic foundation in statistics and provide knowledge of the ideas and tools of practical statistics and their usefulness in problem-solving and decision making. Some of the topics we studied included graphical displays of data, measures of central tendency and variability, sampling distributions, and confidence intervals and hypothesis testing for means and proportions. Our course also heavily focused on how we can use statistics in real life by providing real-world problems.
The first project I have attached is a group project that I completed studying the effectiveness of curving grades and other techniques that are used to assess students’ knowledge of a topic. The next assignment I have included is a paper I wrote describing the statistical procedures I used in order to determine an effective sample size for a hypothetical study of student height that could be conducted at our university.
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Katelyn Housler, Averee Gerold, Olivia Skinner, Layne Fadely, and Jamie Wright
Statistics 171, Project 2
In order to find an estimate sample size for this study, we used the formula M = z. (σ/n)
using our group to calculate the standard deviation. Using the information given in the problem, “M” is the 1 inch which the average height must be within, and “z.” can be found using the 99% confidence level that the problem also gives us. We were able to use the calculator formula, “invNorm(area, , σ)” where the area is equal to the 99% confidence level plus the 0.005 area that is to the left of the 99% under the curve. is equal to zero, with σ being one, so we ended up having a z. equal to 2.576. For standard deviation, we used our group heights to calculate it on the calculator. Layne, Averee, Olivia, and Jamie all were 65 inches tall and Katelyn was 62 inches tall. We then entered this into the “List” function on our calculators and used Variable Statistics to find the standard deviation of the data as well as other numbers such as the five number summary. Once we were able to find all of this information, we plugged it into the formula to get, 1 = 2.576 (1.342/n). We then used algebra to isolate n, and then squared it and 3.458 (on the other side of the equation) to get the sample size equal to 11.949. Since it is not possible to have 0.949 of a person, we would round this number up to 12 to have an estimate sample size of 12 so that the average height is within 1 inch of the population’s mean height.
In order to obtain our sample, we would get a list of all the students enrolled at
Longwood University and would then label all of them 1 through however many there are in order to make the data quantitative for sampling purposes. We would then use the sample size of 12, which we were able to estimate with the formula “M = z. (σ/n)”, to find a random sample from the entire population of Longwood students. To do this, a random number generator such as a TI-84 calculator, would be used to draw 12 randomly selected students from the entire population of Longwood students so we could then find their height. The random number generator will allow the sample to be completely unbiased and as accurate as possible. On the calculator, we went under the math then probability function and used the random integer no repetition option in order to get 12 distinct data values that were both random and completely different from each other. Once we had these numbers, we would find the student corresponding to each number on the list and ask them their height. Following this procedure would ensure that the sample drawn is completely random because we are able to use technology after making the qualitative data of names quantitative by assigning numbers to each.
The only issue with this procedure would be the small sample size that we used. Because the members of our group were all so similar in height, the standard deviation between height data values was much lower than what that of the population of all Longwood students would be. This, in turn, shrinks the estimated sample size to be much smaller than what should actually be used to appropriately represent the population because the standard deviation is used in the formula to estimate the sample size. If this study were to actually be conducted, we would recommend using a larger group to find the standard deviation so that there is a higher likelihood for a difference in height and therefore a more representative standard deviation to be used in calculating a sample size estimate.
NOTE: the term “z.” is used to denote “z-knot” as the appropriate symbol could not be located
for use.
April 12, 2019