• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month
Page
1. 1
1
2. 2
2
3. 3
3
4. 4
4
5. 5
5
6. 6
6
7. 7
7
8. 8
8
9. 9
9
10. 10
10
11. 11
11
12. 12
12

# 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.

The above preview is unformatted text

This student written piece of work is one of many that can be found in our AS and A Level Probability & Statistics section.

## Found what you're looking for?

• Start learning 29% faster today
• 150,000+ documents available
• Just £6.99 a month

Not the one? Search for your essay title...
• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month

# Related AS and A Level Probability & Statistics essays

1. ## The heights of 16-18 year old young adults varies between males and females. My ...

5 star(s)

x^2 F xF x^2F 5ft 2inc 62 3844 1 62 3844 5ft 3inc 63 3969 0 0 0 5ft 4inc 64 4096 2 128 8192 5ft 5inc 65 4225 2 130 8450 5ft 6inc 66 4356 2 132 8712 5ft 7inc 67 4489 3 201 13467 5ft 8inc 68 4624

2. ## I am investigating how well people estimate the length of a line and the ...

Year 7 and 10 Females Groups Frequency Cumulative frequency 0- 19 19 10- 5 24 20- 7 31 30- 4 35 40- 0 35 50- 0 35 60- 0 35 70- 0 35 80- 1 36 90- 0 36 100- 0 36 Cumulative frequency: 36 1/2(36+1)

1. ## Standard addition was used to accurately quantify for quinine in an unknown urine sample ...

By substitution of equation 2 into equation 1 we get This equation containing an exponential term can be expanded as a Maclaurin series. Ultimately the following is derived: At constant P0, F = Kc Thus, a plot of the

2. ## Chebyshevs Theorem and The Empirical Rule

Find an interval for the number of hours volunteered in which at least 88.9% of the students in this program would fit. Solution: From the table above we see that a percentage of 88.9 will coincide with an interval of hours.

1. ## AS statistics coursework - correlation coefficient between height and weight in year 11 boys ...

Sxx = Syy = Sxy = Linear Regression And The Least Squares Regression Line Regression is the process by which you can determine the function satisfied by points on a scatter diagram. The function will give you points that will pass through the mean, (,).

2. ## &amp;quot;The lengths of lines are easier to guess than angles. Also, that year 11's ...

This gives 14.7. This spread is quite high, which means that the estimates given by the year 9's for the size of angle 6 was quite big. You can also see that the year nines had a lower spread of data for the length of line 2.

1. ## My hypothesis is: 'Girls obtain better grades than boys'.

it will not be the sex that you are sampling at that time, e.g. in the table you can see that there are more males which were tested than females. Because the results are all in order before the sample was taken the results for males and females come out very similar.

2. ## Used Cars - What main factor that affects the price of a second hand ...

of car depreciates the fastest and which size of car hold it is value longest. On these graph I also plotted lines of best fit as through finding the equation of the line I can then figure the depreciation. Scatter graphs From the first three scatter graphs I was able to analyse the data from the sample of cars.

• Over 160,000 pieces
of student written work
• Annotated by
experienced teachers
• Ideas and feedback to