Statistical Analysis Project: Internet Speed Analysis Report

This project presents a comprehensive statistical analysis of internet speed data, focusing on the performance of the National Broadband Network (NBN). The analysis includes interval estimation of population proportion to determine the proportion of time with download speeds of 40 Mbps or more, and hypothesis testing to examine the average download speed and the difference in mean download speeds between two tests. Simple and multiple linear regression analyses are performed to explore the relationship between upload and download speeds, as well as the impact of evening time on upload speeds. The project concludes with the determination of the best-fit model and provides interpretations of the regression coefficients and statistical significance. The analysis addresses a friend's concerns about their NBN 50 plan, providing insights into download and upload speeds.

Running head: STATISTICAL ANALYSIS
Statistical Analysis
Name of the Student
Name of the University
Course ID

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Table of Contents
Email................................................................................................................................................2
Appendices......................................................................................................................................7
Question 1....................................................................................................................................7
Question 2....................................................................................................................................8
Question 3....................................................................................................................................9
Question 4..................................................................................................................................11
Question 5..................................................................................................................................13
Bibliography..................................................................................................................................17

2STATISTICAL ANALYSIS
Email
From: [e-mail]
To: [e-mail]
Subject: Statistical analysis of internet speed
Dear Steve,
In your last mail you have asked for further clarification regarding internet speed in the
National Broadband Network. To make a clearer understanding about internet speed some
further statistical analysis has been conducted for reaching out some meaningful conclusion.
Estimate of proportion of time with download speed of 40 Mbps or more:
Table 1: Interval estimation of proportion
The first concern is related whether the download speed is 40 Mbps or more, which is
80% of the speed of 50 Mbps as theoretically claimed on NBN. From the 120 randomly collected
sample the proportion of time where download speed is at least 40 Mbps or more is obtained as

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0.87. Using the sample estimates of proportion, it is obtained that the proportion of this time
varies between 81.58% and 93.42% in 95% of the cases.
Test of average download speed
Table 2: Sample mean test
Analysis has been made to examine whether average evening download speed is more
than 41 mbps. Hypothesis test has been performed to make any inference in this regard. Result of
the inferential test suggests the claim that average download speed is more than 41 mbps is
correct. Therefore, any user connected with NBN can enjoy an average download speed of more
than 41 mbps in evening.

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Difference in mean download test
In order to make a much stronger inference about the internet speed a second speed test
has been made. The sample data set thus contains two sets of result for download speed test.
Given the sample is taken randomly, the average download speed should be same. In other
words, the difference in average download speed between test 1 and test 2 should be zero.
Hypothesis test has been performed to test the proposed assertion that two test gives same
average download speed.
Table 3: Result of two independent sample mean

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The result shows that there is no statistically significant difference in download speed
between the two tests. Therefore, you can be sure that each of your speed test gives same
download speed.
Simple linear regression
Another area of interest regarding internet speed on NBN is the relation between upload
and download speed. To examine the relation first a simple linear regression analysis is
performed
Upload speed=3.474+(0.295× Downlad speed )
The measure of correlation coefficient helps to understand the association between
upload and download speed. The correlation coefficient is 0.77 indicating a strong positive
association between upload and download speed. From the obtained regression equation the
value of intercept is 3.474. That means, you can have an average upload speed of 3.474 Mbps
with zero download speed. The slope value of the regression line is 0.295. Positive slope value
suggests upload speed varies positively with the download speed. If download speed increases by
1 percent then upload speed increases by 0.30 percent. Both intercept and slope are statistically
significant. The coefficient of determination for the simple linear regression model is 0.60. This
implies that Download speed accounts 60 percent variation in the Upload speed.
Multiple linear regression
Upload speed often varies with time. In order to model the impact of time specifically
evening time a new model is developed adding ‘Evening’ time.

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Upload speed=3.490+ ( 0.416 × Evening ) +(0.291 × Download )
The coefficient of determination for the new model is 0.61 meaning Evening time and
Download speed together account 61 percent variations in the upload speed. The intercept value
is 3.490 meaning that during any time except evening with a zero download speed, the average
upload speed is 3.490. The coefficient of evening is 0.416 implying that upload speed likely to
increase by 0.416 during evening. The coefficient of download speed is 0.291 which is smaller
than that obtained in simple linear model. This indicate in the model the impact of download
speed on upload speed is smaller compared to the previous model. The relation between evening
time and upload speed however is not statistically significant meaning that the variable can be
dropped to get a better model. The simple regression equation therefore fits the data best.
Hope the analysis and discussion will address all your concern related to internet speed
on NBN.
Regards,
Maria Smith

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Appendices
Question 1
Technique: Interval estimation of population proportion
Random variables
T: Number of times with download speed of at least 40 Mbps.
n: Number of observation in sample
^P: Proportion of time when speed of download is equal or more than 40 Mbps.
Proportion of time with download speed 40 Mbps or faster is obtained as
^P= Number of time download speed is 40 Mbps∨faster
Total number observation ∈sample
Excel output

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Conclusion
From the 95% confidence interval it can be concluded that proportion of time with
download speed of at least 40 Mbps lies between 81.58% and 93.42%.
Question 2
Technique: Hypothesis test for sample mean
Random variables:
x: Sample mean for download speed in evening
n: number of observation in the sample
μ : Population mean for speed of download in evening
Hypotheses
Null Hypothesis (H0):
μ ≤ 41
Alternative Hypothesis (H1):
μ> 41
Level of Significance
The chosen level of significance for the test is 5% or 0.05.
Test statistics
The suitable test statistics for the hypothesis test is ‘t’ statistics (since population variance
is unknown).

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Excel output
Conclusion
P value is 0.0000 which is smaller than the significant value implying rejection of null
hypothesis. This suggests acceptance of the claim that mean download speed is above 41 Mbps.
Question 3
Technique: Hypothesis test for equality two independent sample mean.
Random variable
x1: Average speed of download from speed test 1

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x2: Average speed of download from speed test 2
μ1 : Population mean of speed test 1
μ2 : Population mean of speed test 2
n1=n2=120
σ 1 , σ2 Unknown
Hypotheses
Null Hypothesis (H0): Mean download speed is same for two tests
μ=0
Alternative Hypothesis (H1): Mean download speed is greater than 41 Mbps.
μ ≠ 0
Excel output

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Conclusion
Obtained p value for the test is 0.9293. The p value is larger than 5% significance value
meaning acceptance of null hypothesis that there is no significant difference in mean download
speed between two tests.
Question 4
Simple linear regression
Figure 1: Scatter plot
A positive linear relation is obtained between speed of upload and download from the
above scatter diagram.
Variables
Dependent variable: Upload speed
Independent variable: Download speed