- Level: AS and A Level
- Subject: Maths
- Word count: 2576
Compare the heights of girls and boys in year 8 and the sixth form.
Extracts from this document...
Introduction
INTRODUCTION TO TASK & HYPOTHESIS The purpose of this exercise is to compare the heights of girls and boys in year 8 and the sixth form, in an attempt to show the following. That in year 8, girls and boys will have more similarities in height, but girls are more likely to be taller than the boys. In sixth form there will be greater differences between the heights of boys and girls and the boys are more likely to be taller. That there will be a much greater difference in the heights of boys between year 8 and sixth form than between the girls. I will attempt to show this by measuring the heights of boys and girls in year eight and the sixth form. In each case a sample size of fifty will be used in order to produce statistically valid results according to the central limit theorem. This will be done, by obtaining a sample that accurately represents each group. Firstly a list of boys and a list of girls in year eight and the sixth form will be formulated giving each student a number. Then a random number generator will be used to select fifty boys and fifty girls from each year group. I will measure the selected groups independently using the measuring device illustrated below. ...read more.
Middle
Standard error The standard deviation of the distribution of sample means is called the standard error. 1 s.e = ?�/n (variance of the distribution of x = ?�/n) In previous calculations I have only worked out the mean x and variance s� of my sample. I cannot calculate confidence intervals for population mean � because I do not know ?�. Unfortunately s� is not an unbiased estimator of ?� (i.e. the mean of the distribution of s� is not equal to ?�). However Is an unbiased estimator of population variance, and I can use this as an estimate of ?� when calculating standard error in order to produce confidence intervals for �. So in order to calculate the standard errors for each of my groups I must first calculate an estimate for ?�, using the above formulae. CALCULATIONS FOR THE ESTIMATES ?� AND STANDARD ERRORS I have previously calculated the mean (x) and standard deviation (s�) for each of my groups. I will now calculate an estimate for ?� in order to calculate the standard errors and formulate confidence intervals for each of my groups. To estimate ?� I will use the previously stated formula. And then using these estimates for ?� I will calculate the standard errors using the formula. CONFIDENCE INTERVALS If we have one sample mean x then P(� - 1s.e < x < � + 1s.e), but this can ...read more.
Conclusion
The accuracy of my results would improve by using a larger sample size e.g. 100 girls and boys from each year group, according to the central limit theorem. However, this was not possible due to the amount of people available to measure and the amount of time allocated. I could have improved the sample further by taking groups of students from different schools in different areas, this may have given a more accurate representation of the population, as the ranges of heights in different areas for each group may be more varied. However this would have been very difficult to do and would have taken too long, also I don't think it would have shown any great difference in my findings, as the heights of boys and girls in each group throughout the region are most likely to be fairly similar to those I measured. If I had had more time it would have been interesting to find out where exactly the changes in the heights of boys and girls actually occurs. This could have been done by taking a sample of fifty girls and fifty boys from each of the years in between year eight and the sixth form, and again calculate confidence intervals to see when the boys go from being the same height or shorter than the girls to being much taller than them. ...read more.
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