Hypothesis 2
Right-handed students are faster than left-handed students are
I will again use stratified sampling, to find a fair number of left-handed and right-handed students that I need to total 50, out of the 307 year 10 students. There are 234 right-handed students, and 73 left-handed people.
To select the 38 right-handed students and the 12 left-handed students, I will pick every 4th person, as I did for hypothesis 1.
Hypothesis 3
Right-handed boys are faster than right-handed girls are
Out of the 307 year 10 students, 127 are right-handed boys, and 107 and right-handed girls. To find the proportion of right-handed boys and girls that I need to make 50 I will again use stratified sampling.
To select my 27 right-handed boys and 23 right-handed girls, I will pick every 4th person from the data bank.
Testing
Hypothesis 1
Boys are faster than girls are
I found the averages for my sample of 50 students, and decided to arrange the results into grouped-data tables for convenience and accuracy. My groups were decided as: -
Reaction (cm’s)
0-5 extremely fast
5-10 fairly fast
10-20 average
20-25 slow
- Very slow
The results for boys were as follows-
The results for girls were as follows-
I will use a cumulative frequency graph with the inter-quartile range and box-plots. I will use A Cumulative Frequency Graph as I will be able to compare ranges (I.Q.R.), find the median and aid with boxplots to identify outliers and show skewness. As I expect the boys’ reaction to be faster than the girls’ I will expect the line representing the boys to be steeper than the line representing the girls.
Testing
Hypothesis 2
Right-handed students are faster than left-handed students
I found the averages for my sample of 50 students, and decided to arrange the results into grouped-data tables for convenience and accuracy. My groups were decided as: -
Reaction (cm’s)
0-5 extremely fast
5-10 fairly fast
10-20 average
20-25 slow
25-30 very slow
The results for right-handed students were as follows-
The results for left-handed students were as follows-
I will use a Histogram, to find the median. As I expect the right-handed students to be faster, I will expect the median for the right-handed students to be lower than for the left-handed students.
Right-handed Median = 13.5
Left-handed Median = 15
Conclusion for Hypothesis 2
The medians again prove that my 2nd hypothesis is correct. Right-handed students are faster than left-handed students because the right-handed students achieved a median of 13.5 whereas the left-handed students achieved a median of 15, making the right-handed students’ average faster.
Testing
Hypothesis 3
Right-handed boys are faster than right-handed girls are
I found the averages for my sample of 50 students, and decided to arrange the results into grouped-data tables for convenience and accuracy. My groups were decided as: -
Reaction (cm’s)
0-5 extremely fast
5-10 fairly fast
10-20 average
20-25 slow
- very slow
The results for right-handed boys were as follows-
The results for right-handed girls were as follows-
The estimated mean for right-handed boys is 13
The estimated mean for right-handed girls is 14
Conclusion for Hypothesis 3
The estimated mean for the right-handed boys is 13 whereas the estimated mean for the right-handed girls is 14, this means that the boys are faster because they have a faster average than the girls do. This proves my 3rd hypothesis correct
I used the estimated mean in order to get an immediate result of who is faster out of everybody. It also means I will be able to find the standard deviation (page 7 & 7a).
Testing
Hypothesis 3 (continued)
Although I have already proved the 3rd hypothesis correct, I am going to put the data into a histogram, to secure my conclusion.
The tables of results were arranged in the same way
Right-handed boys-
Right-handed girls-
The Medians
Right-handed boys = 12
Right-handed girls = 13.5
Conclusion for 2 for hypothesis 3
I can see from the Medians, which I read off of the histograms, that Right-handed boys are faster than Right-handed girls are. The right-handed boys’ median was 12 whereas the girls’ median was 13.5 making the right-handed girls slightly less- faster than the boys are. This proves my 3rd and final hypothesis right for the second time.
Testing
Hypothesis 3 (continued 2)
The estimated mean for boys = 13
The estimated mean for girls = 14
The method of how I found the estimated means, is on page 5
The standard deviation for the right-handed boys is (to 3 s.f.): 4.48
The standard deviation for the right-handed girls is (to 3 s.f.): 5.26
Conclusion 3 for Hypothesis 3
The standard deviation value of the right-handed boys is lower, which means that the right-handed boys are more consistant
Also I can see from the Standard deviation methods on page 7a, that 95% of the right-handed boys’ reaction ranged between 4.04cm and 21.96cm whereas 95% of the right-handed girls ranged between 3.48cm and 24.52cm, this again shows that the boys are more consistent. I expect to find the median and expect of the boys to be lower than the girls.
Further improvements
If I were to do this investigation again, I would re-do Hypothesis 1. I would find and remove the outliers from the data, and re-construct my cumulative frequency graph, to see if it altered the results, which I have found.
Also I would place the data for each hypothesis, into other forms of graphs (i.e. histograms for hypothesis 1, cumulative frequency for hypothesis 2 etc). This would ensure that my conclusions are more precise and correct, as I did for hypothesis 3 where I used the estimated mean, a histogram and then found the standard deviation.
Furthermore, I would test other hypotheses such as Right-handed girls are faster than Left-handed boys are etc. I could also change the age group, and see if I get different results to what I have, for each hypothesis. Another thing I could change is the form of test, so instead of dropping the ruler I could try the stopwatch experiment.
Overall Conclusion
After analyzing all of the results from the tests for all 3 hypotheses, I can see that my hypotheses were correct. For hypothesis 1, the Median for the boys was 10 whereas the median for the girls was 13. This meant that the boys were faster than the girls were. Also the box plots and the steepness’ of the lines from cumulative frequency graph showed the boys were faster.
For hypothesis 2, the Right-handed students proved to be faster than left-handed students because the right-handed students had a median of 13.5 whereas the left-handed students achieved a median of 15. This meant that right-handed students’ average was faster.
For the 3rd hypothesis the boys estimated mean was 13 whereas the girls estimated mean was 14. This showed that the right-handed boys’ average was faster than the right-handed girls’ was, making the right-handed boys faster.
I also put the data into a histogram. The Median for the right-handed boys was 12 whereas the right-handed girls, was 13.5. This proves again that the right-handed boys were faster than the right-handed girls were.
I found the standard deviations for the right-handed girls and boys. It showed that the boys were more consistent than the girls were.
Conclusion for Hypothesis 1
The Median for the boys is 10 whereas the median for the girls is 13. This already proves my hypothesis correct boys are faster than girls are.
Also, on the box-plots ¾ of the boys have a reaction between 10 and 13 whereas ¾ of the girls have a reaction between 13 and 17, so the majority of boys are faster than the girls are.
I can also see from the whiskers of the box plots that there are outliers. There is a boy who is extremely slow in comparison to the majority of the boys and a girl who is also extremely slow in comparison to the majority of the girls.
The steepness of the boys’ graph proves again that the boys have a faster reaction than the girls do.
Furthermore, I can see from the inter-quartile ranges, (which represent the middle-half of the sample) that the girls are slower, the reaction of the middle half being 6.5 and the boys’ being 4.5.
In addition to this, I can see from the inter-quartile ranges that the boys are more consistent as their range is closer together 8.5 – 13 compared to the girls ranging from 10.5 - 17