Testing a Hypothesis about Male and Female Drivers
My initial thoughts on the data are that it seems that more females
are taking driving lessons than males as seen in the pie chart below.
It would also seem that as the number of 1hour lessons increases the
number of minor mistakes made decreases. Instructor B looks to be the
most popular as he is chosen the most out of the four. I am going to
state 3 hypotheses based on this data and am going to use my
mathematical knowledge to support them.
Hypothesis 1: Females make more Mistakes than Males
For this hypothesis I decided to choose 60 pieces of data from the
sheet, 30 pieces that are male and 30 that are female. I used the
random number button on my calculator and multiplied it by 240 (the
total pieces of data) this insures that the number is between 1 and
240, the number that comes up must be rounded to the nearest whole
number this number is then used to pick the relevant number from the
sheet. Once 30 pieces of data had been collected for the males and I
had not yet got 30 for the females, I continued using my calculator
until I got a number that corresponds with a female piece of data on
the sheet. Once I had 30 for each I started to refine the data.
I started by taking the 30 male pieces of data and 30 female pieces of
data and plotted them on a line graph seen below.
From the line graph I found that it was a male who made the highest
amount of mistakes but also a male who made the lowest amount of
mistakes. By looking at the graph I also found that a greater number
of females were found to be greater than that of the males.
I then proceeded to make 2 cumulative frequency curves. I did this by
taking the 30 pieces of male data and grouping them by finding out how
many mistakes each male made them adding him in the corresponding
group shown below. After getting the groups and the number of males
for each group (frequency) I found the cumulative frequency for each.
I got this by adding every frequency before each group (for the last
group you should get 30 – the total amount of data). I then repeated
these steps with the female’s data and am now ready to plot the
graphs. To plot the graph I then took the number of the upper bound of
each group and the cumulative frequency and plotted them accordingly.
For each graph I found the median by halving the total frequency then
drawing a line across from to smooth curve drawn in the middle and
down to be read of at the bottom. I also found the upper and lower
quartiles by dividing the total frequency by 4 to get the lower
quartile and by multiplying the total frequency by 3 and dividing by
four to get the upper quartile. With the lower and upper bounds we
could also find the inter quartile range by subtracting the lower
bound from the upper bound.
From the graphs...