Sample Mean and Standard Deviation

SAMPLE MEAN AND STANDARD DEVIATION 1
Research and Hypothesis Testing
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SAMPLE MEAN AND STANDARD DEVIATION 2
Using Sample Mean and Standard deviation
In recent years, there has been a rise in cases of obesity and overweight in many parts of
the world including Australia. Height and weight are important measures that are important in
the computation of the body mass index (BMI) of an individual. This is an important issue since
obesity and overweight are associated with heart diseases, diabetes, high blood pressure, gout
among others. The study sought to find out if there exists a significant difference in the mean
weight of Australians. According to the Australian Bureau of statistics, in the year 2012, an
average Australian woman measured 161.8 cm and 71.1kg in weight while men weighed 85.9
kg. A random sample of 10 female students was taken and their weights measured using a
weighing machine.
Hypothesis tests
A hypothesis is classified as an educated guess that any researcher is interested at finding out.
The null hypothesis is the one the researcher assumes no difference between the test variables
while the alternative hypothesis test the existence of a difference between the two.
Null hypothesis (Ho ):The sample mean weight of female students is not different from the
normal population. (Ho=0)
Alternative hypothesis (HA ): The sample mean weight of female students is different from the
normal population (Ha ≠ 0)
The table of female weights is as shown below.
Table 1: Sample Data set
Student Female Weight (Kgs)
1 80.5
2 60.9
3 73.4
4 75.0
5 70.0

SAMPLE MEAN AND STANDARD DEVIATION 3
6 65.0
7 67.8
8 72.1
9 89.0
10 60.2
SUM 713.9
MEAN 71.4
STD DEVIATION 8.83
Considering that Sample Mean formula is = X = ∑ X
N = 80.5+60.9+...+ 60.2
10 =71.4
Sample standard deviation ( s ¿ formula = √ ¿ ¿=8.83
The sample statistics is t= X−μ
S / √N where X =71.1kg,μ=¿71.4kgs s=8.83 and n=10
Therefore sample statistics t= 71.1−71.4
8.33/ √ 10 =-.1039
The considered level of significance is 5 %.We are therefore testing if sample and population are
greater than 95%.
From the t-distribution table, checking the critical value t0.05,9 = 2.262 for the two tailed test
which is our concern.
Since the critical value is 2.262, the value of -.1039 which is less than the critical value. The null
hypothesis is therefore accepted.
Justification
We, therefore, conclude that the sample mean weight of female students is not different
from the normal population. According to the Australian Bureau of statistics report of 1995, the
majority of males with age above 18 years of (56%) while the majority of females (60%) were
2.262