Statistical Analysis: T-Test on Surface Area of Dog's Mercury Leaves

This assignment focuses on performing and interpreting a t-test to analyze the surface area of dog's mercury leaves. The student begins by stating the null and alternative hypotheses, then performs a t-test on two samples: shade leaves and sun leaves. The assignment includes calculations of means, variances, and t-statistics, along with the interpretation of p-values to determine whether to reject or fail to reject the null hypothesis. The experiment's aim is described, along with the method of data collection, followed by a restatement of the hypotheses. The importance of the significance value in the t-test is also discussed, highlighting its role in indicating the risk associated with the results and guiding the acceptance or rejection of the hypotheses based on the p-value compared to the alpha value. The analysis concludes that there is no statistically significant difference in the mean values of the surface area of shade and sun leaves of dog’s mercury.

Part 3 - Performing t- test
statistics

Table of Contents
TASK 1............................................................................................................................................1
a. Stating hypothesis....................................................................................................................1
B. Performing t-test on both the samples.....................................................................................1
TASK 2............................................................................................................................................1
a) Description of aim of the experiment and method of data collection.....................................1
b) Stating Hypothesis...................................................................................................................2
TASK 3............................................................................................................................................3
Importance of Significance value................................................................................................3

TASK 1
a. Stating hypothesis
Null hypothesis (H0): There is no significant difference in the mean values of surface area of
shade and sun leaves of dog’s mercury.
Alternative hypothesis (H1): There is a significant difference in the mean values of surface area
of shade and sun leaves of dog’s mercury.
B. Performing t-test on both the samples
T-Test: Two-Sample Assuming Unequal Variances
(Site A) (Site B)
Mean 18.25 16.08
Variance 9.11 6.63
Observations 12 12
Hypothesized Mean Difference 0
df 21
t Stat 1.89
P(T<=t) one-tail 0.036
t Critical one-tail 1.72
P(T<=t) two-tail 0.072
t Critical two-tail 2.079613837
On the basis of above assessment, we do not reject null hypothesis because 1.89 < 2.08
respectively. Hence, considering the results of T test it can be mentioned that null hypothesis is
true or appropriate. As per results, no statistically significant difference takes place in the mean
values of surface area of shade and sun leaves of dog’s mercury
TASK 2
a) Description of aim of the experiment and method of data collection
The main aim of this experiment is to analyse surface areas of leaves per centimetre square
for dog’s mercury. In order to perform his function, two shades have been chosen. Site A is with
12 deep shade leaves and Site B with 12 open sunlight leaves. The data has been collected
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considering two situations for plants. One where they are shade leaves and the send when they
are open sunlight leaves. The area in centimetre square has been taken into notation so as to find
out the results and perform test on it.
b) Stating Hypothesis
Null hypothesis (H0): No significant difference in mean values of surface area of shade and sun
leaves of dog’s mercury.
Alternative hypothesis (H1): Significant difference in mean values of surface area of shade and
sun leaves of dog’s mercury.
T test helps in preparing analysis of two population mean with the help of statistical
examination. Two samples of smaller size are taken into consideration so as to analyse its
dependence. The calculated mean value of site A is 18.25 and that of site b is 16.08. the
difference in value of variance is quite wide. It is 9.11 for Site A, where leaves where picked
from shed. However, it is 6.63 for Site B when it was picked through open sunlight. T value
calculated through one tailed test helps in measuring size of the difference relative to variation in
sample data. The calculated value of T in one tailed test is 0.036. In this scenario, H0 will be
accepted, indicating that there is not significant difference between mean values of surface area
of shade and sun leaves of dog’s mercury. However, in case of two tailed t test performed, it can
be analysed that the value of T calculated is 0.072. P value is greater than alpha, which is 0.05.
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Hence, in this scenario, alternative hypothesis will be accepted. Hence, it can be stated that there
is significant difference in mean values of surface area of shade and sun leaves of dog’s mercury.
TASK 3
Importance of Significance value
Significance value plays an important role while conducting T test. It helps in indicating
the risk involved in overall results received. The value of P higher than value of alpha indicates
that alternative hypothesis is rejected and null hypothesis is rejected. However, in case of P value
lower than alpha value, then null hypothesis is accepted and alternative hypothesis is rejected.
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