Body Measurements – Math 1040 Final Project
Throughout this semester we have been evaluating claims and looking at statistical analysis’ of populations data. For my final project I chose to evaluate data on a population of individuals who participated in a study of their body measurements. There were 507 individuals that participated in the study; from the population I then drew two samples of 33, one being a simple random sample, and the other being a systematic random sample.
Firstly, I examined the populations’ categorical data – male to female ratio, which was 248:259, which was 49% male to 51% female. In sample 1, the simple random sample, the ratio was split 16:17, which was 48% male to 52% female. In sample 2, the systematic random sample, the ratio was split 17:16, which was 52% male to 48% female. Although, the populations were not evenly split between male and female like one would assume, with an uneven sample number it is mathematically impossible to have the samples be evenly split.
The confidence intervals for population proportion, of the categorical data, the ratios of male to females in sample 1. These intervals are 90% (0.372, 0.658), 95% (0.345, 0.686), and 99% (0.291, 0.739). Meaning that in each interval, we are X% confident that the population proportion of females will be included in the confidence interval. In all of our intervals we can be confident that the population proportion of females, which are 51.52% will be between the values (0.372, 0.658). The values all worked, because the sample data did a good job of estimating the population value.
I ran a hypothesis test on categorical data of sample 1, to test and see if the population proportion is equal to 50% (Ho: p=0.50, H1: p≠0.50). With a two-tailed test the p-value is twice the value of the area to the right; the p-value is 0.8650.The calculated p-value is 0.8618, both of the p-values are greater than significance levels of 0.01, 0.05, and 0.1; therefore we fail to reject the null hypothesis. Thus we can conclude that there is not sufficient sample evidence to warrant rejection of the claim that 50% of the population is female.
Secondly, I examined the populations’ quantitative data. I chose to evaluate abdominal measurements, as I am going into the health care field, and abdominal measurements can tell us a lot about the individual. The frequencies within the population were normally distributed, the mean was 85.654cm with a standard deviation of 9.415cm, minimum of the population was 64cm, and the maximum was 121.1cm. The frequencies within sample 1 were skewed to the right, the mean was 84.5cm with a standard deviation of 9.244cm, the minimum of the sample 67cm, and the maximum was 107cm. The frequencies within sample 2 were skewed to the left, the mean was 79.345cm with a standard deviation was 15.175cm, the minimum was 52.4, and the maximum was 107.3cm.
The confidence intervals for population mean, of the quantitative data, abdominal girth of sample 1 where the mean was 84.5, and sample standard deviation was 9.244, and the population standard deviation is “unknown”, three confidence intervals are computed as below. For this sample the confidence intervals are 90% (81.774, 87.226), 95% (81.222, 87.778), and 99% (80.094, 88.904). Meaning that in each interval, we are X% confident that the true mean of abdominal girth for all of the people in the population, will be included in the confidence interval. The population parameters of a population mean 84.5 and a standard deviation of 9.244 is captured by all of the confidence intervals, we can continue to create a narrower confidence interval, however the degree of confidence that will be displayed decreased substantially with every attempt to narrow our interval.
I ran a hypothesis test for the abdominal girth in the sample 1, we tested the claim that the population mean is greater than 1st Quartile of the population (Ho: mµ=78.8, H1: mµ>78.8). The sample is right-tailed; therefore the critical region is everything right of the critical value (everything greater than 1.694). The test statistic 3.542 is greater than 1.694, it is in the critical region, so we reject the null hypothesis. There is sufficient evidence to support the claim that the population mean is greater than 78.8cm.
This project helped me understand the concepts of statistical analysis, and testing. Throughout the statistical projects of this class I have learned a lot about how Math, and Statistics relates to treatment in the health care world. I asked around while working on projects for this class “how many times have you used statistics since learning it in class” and was slightly depressed (just kidding) when I heard a resounding, “we use it everyday, even if we are not the ones doing the math or data collection – medicine relies on statistical analysis.” Through this project it helped me get a first hand experience of forming a hypothesis, sample selection, analyzing said data, interpret the data, and in turn being able to reject or approve our hypothesis.