Large Population

Large Population

Introduction:

The aim of this study is to establish the relationships between eye color, index figure length and gender, the population selected was the college students and staff, due to the large population it was necessary to select an appropriate sample, a sample of 120 students was appropriate for this study and data regarding gender, figure length and eye color using collected through observation.

Method:

The total population was established to be 11, 394 and due to time limitations we decided to come up with a stratified sample of 120 participants, consistent of data collected by individual members was ensured by deciding that all the length values were to be in millimeters, accuracy and consistence was also achieved by deciding that measurements were to be done by sliding the ruler between the index and middle finger with the units lying along the index finger and measure from the base to the top, excluding the figure nail. Thus accuracy was ensured as all group members were using the same units of measurements to measure the same portion of the finger and taking those measurement in the same way reducing the number of variations in measurement.

Sampling:

A stratified sample was obtained by taking into consideration the various age groups and age in the population, the sample size for each stratum was determined by dividing the population of the strata by the total college population and then multiplying the result by 100, the following table summarizes the population of the college:

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College population:

Age

Male

Female

Total

% Male %Female

% Age Group

16-19

1950

1735

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3685

17%

15%

32%

19+

4010

2880

6890

35%

25%

60%

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staff

480

339

819

4%

3%

7%

Total

6440

4954

11394

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57%

43%

This data in this table can be summarized in a chart as follows:

Sample:

The sample size for each stratum was then determined by dividing the size of the strata by the total population and then multiplying by 120, the results were as follows for each stratum:

calculated sample

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Age

Male

calculated

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female

calculated

16-19

1950

20.537125

1735

18.2727751

19+

4010

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42.232754

2880

30.3317536

staff

480

5.0552923

339

3.57030016

sample to be used:

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Age

Male

female

16-19

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21

18

19+

42

30

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staff

5

4

grand total

total

68

52

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120

The percentage of the sample for each stratum can be summarized by the excel chart below:

Data collected:

After data was collected there was a need to draw various conclusions regarding the data, results were then classified into male and female, then age groups which were those aged between 16 to 18 years, 19 years and above and finally the staff.

Gender:

Of the 120 participants 68 were male while 52 were female, this means that 43% were female while 57% of the respondents were male; the chart below describes the distribution of our sample:

Age groups:

The data was further analyzed according to age groups, this included the age group 16 to 18 years, 19 and above years and finally the staff, this age group would help establish the distribution of the sample, from the data it was also noted that among the male participants 21

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were between the age group 16 to 18 years, 42 participants were 19 and above old while only 5 were staff members, the chart below summarizes this observation:

Natural eye color:

The data was also stratified into their natural eye color, Like gender eye colour is a discrete variable that can be counted and compared. The chart below illustrates that the majority of particpants had brown eyes followed by blue, then hazel and finally green:

Index figure length:

We also analysed the mean length for ech group, it was evident that participants aged between 16 to 18 years had a large mean length, it was evident that the staff mean length was the lowest, this signifies that as the individual grow the length of their index fingure declines, the chart below summarises the mean values for each age group:

Natural eye color:

Of the 120 participants 42 had blue natural eye color, 12 had green natural eye color, 48 had brown natural eye color while only 20 had hazel natural eye color, and this means that the majority of the respondents had brown natural eye color.

Results:

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The table below summarizes the figure length mean for male and female; it also contains the median, standard deviation, maximum value, minimum value and the variance

index figure length

male

female

mean

75.42029

71.92453

standard deviation

6.283512

6.284441

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variance

39.48252

39.49419

median

76

71

max

90

89

min

54

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59

mode

76

71

Distribution:

Using the median, the mean and the max and minimum value we can determine the distribution form for male and female regarding length of the index figure. The mean length of the index figure is 75.42, the median is 76, the maximum value is 90 and the minimum value is 54, for the female the men value is 71.92 standard deviation is 6.28, the median is 71 and the maximum and minimum values are 89 and 59 respectively, according to the mean values it is evident that the mean value of males is greater than the mean value of female, according to the table it is also clear that the standard deviation value is relatively equal for both male and female.

When the mean, mode and median are equal then we refer to such a distribution as a normal distribution, in the male distribution the mode and median are equal but the mean is not equal to

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the mode, for the female case the median and mode are equal but the mean is not equal to the mode, however due to errors associated with samples the difference in the mean and the mode are slight in both cases and therefore we can conclude that in both cases there is a normal distribution.

Male and female values:

The mean value for the male is greater than that of the female, it is also evident that the median value for the male is greater than that of the female, however the standard deviation value for the male and female are approximately equal, a similarity between the two is that they both have normal distributions.

Regarding eye color the following chart summarizes the results of the totals in both cases in terms of percentage values:

Blue

Green

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Brown

hazel

male

38%

12%

39%

12%

female

30%

8%

40%

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23%

From the above table it is clear that majority of male have brown eyes, majority of women also have brown eyes, however according to this sample more females have hazel eyes which is 23% compared to 12% of male, less females compared to males have green eyes with only 8% of the females having green eyes while 12% of the male having green eyes. This data can be summarized in a chart as follows:

Inter quartile range:

According to the excel output the following table summarizes the quartiles, however the inter quartile range can be determined by subtracting the first quartile from the third quartile as follows:

77–70=7

The inter quartile range is therefore 7

1st quartile

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70

2

73.5

3rd

77

4th

90

nd

(median)

From the interquartile range for the index figure length, it is clear that the data is skewed to the right; this means that the data takes the following shape compared to the normal distribution:

Standard deviation and variance for the entire data:

The table below summarizes the standard deviation and variance for the entire data collected

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on the sample, the mean value is 73.901, the variance is 42.188 and the standard deviation is 6.49. according to the central limit theory as the number of random independent variables increase then the distribution of their sum tend to be normally distributed, this means that 95% of the observations will lie between 2 standard deviations, in this case we tend to investigate if this is true with our case, the values from our data can be summarized below:

mean

73.901639

variance

42.188592

standard deviation

6.4952746

median

73.5

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mode

71

Normal distributions have equal mean, median and mode, in our case none of this is true and for this reason we conclude that our distribution is not normally distributed, for this reason therefore the 95% of information being 2X standard deviation does not apply. The standard deviation is a measure of dispersion; it is therefore evident that data deviates 6.49 units from the mean given a normal distribution.

Summary of findings:

Given the entire data it is clear that it is not normally distributed, however when we consider female and male separately then we find out that in both case it is a normal distribution. It is also clear that the males have longer index figure compared to the females.

Hypothesis test:

Hypothesis:

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The male and female index figure length is the same:

Null hypothesis:

H0: b1 =b2 or b1 –b2 = 0

Where b1 is the mean for the males and b2 is the mean for the females

Alternative hypothesis:

Ha: b1≠ b2

We then get our t calculated and t statistics at 5% level of test.

T calculated = (b1 –b2)/ (Sb1/n + sdb2/n) ½

B1 – b2 = 3.495762

(Sb1/n + sdb2/n) ½ = 0.320961

(b1 –b2)/ (Sb1/n + sdb2/n) ½ = 10.89154

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Because our T calculated is greater than T critical at 5% we reject the null hypothesis, by rejecting the null hypothesis we are stating that b1≠ b2 or b1 > b2. For this reason therefore we can conclude that index figure for male are longer than those of female.

References:

Allan Bluman (2000) Elementary Statistics: A Step by Step Approach, McGraw Hill press, New York

Daniel Bridge (1993) Statistics: An Introduction to Quantitative Research, Rand McNally publishers, Michigan

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