Statistical Analysis Project: Internet Speed Data - MAT10251

This project presents a comprehensive statistical analysis of internet speed data, focusing on the performance of NBN. The analysis includes interval estimation to determine the proportion of time NBN meets its download speed commitments, hypothesis testing to assess if evening download speeds are greater than advertised, and tests for equality of means between speed tests. Furthermore, simple and multiple linear regression analyses are performed to explore the relationship between upload and download speeds, and the impact of evening time on upload speeds. The findings reveal the limitations in meeting advertised speeds and the factors influencing upload speed variations. The project concludes with model selection and a bibliography of relevant statistical resources.

Running head: STATISTICAL ANALYSIS
Statistical Analysis
Name of the Student
Name of the University
Author note

1STATISTICAL ANALYSIS
Table of Contents
Part B: Further Analysis of Data- Using Statistical Inference and Regression Analysis...........2
Email..........................................................................................................................................2
Appendices.................................................................................................................................5
Answer 1................................................................................................................................5
Answer 2................................................................................................................................6
Answer 3................................................................................................................................9
Bibliography.............................................................................................................................16

2STATISTICAL ANALYSIS
Part B: Further Analysis of Data- Using Statistical Inference and Regression Analysis
Email
From: [e-mail]
To: [e-mail]
Subject: Internet speed analysis of NBN
Dear Emma,
In context of your concern regarding NBN’s upload and download speed, I would like
to inform you that certain statistical analyses have been performed. Results derived from the
statistical analysis are expected to provide a clearer picture of internet speed of NBN.
You have first asked to estimate the proportion of time when NBN has achieved a
download speed of at least 40 Mbps. The interval estimate for the required proportion gives
the following result
Table 1: Statistical result of interval estimation for proportion

3STATISTICAL ANALYSIS
From the sample estimate it is obtained that the proportion of time when NBN fulfills
its commitment to offer a download speed of at least 40 Mbps is very less. The proportion
varies within the range between 7.93% and 20.41% as can be said with 95 percent
confidence.
The advertised typical evening download speed is 41 Mbps. You have expressed your
concern regarding whether evening download speed is greater than that claimed in the
advertisement. Conclusion has drawn based on the following statistical result of sample mean
Table 2: Statistical result of test for mean evening download speed
The test result indicates that in the evening the average download speed does not
exceed 41 Mbps. It is therefore unlikely that users of NBN can enjoy a download speed of 41
Mbps or faster during evening.

4STATISTICAL ANALYSIS
With the objective of checking accuracy of the speed test 1, a second speed test has
been done. A firm conclusion can be made about download and upload speed only when
average speed does not differ significantly between the two tests. Average download speed
between speed test 1 and speed test 2 has been compared by testing equality of mean for
independent sample.
Table 3: Statistical result for test of equality of mean
The result indicates no significant difference in average download speed between
speed test 1 and speed test 2.

5STATISTICAL ANALYSIS
For determining the relation between upload and download speed simple linear
regression analysis has been done which gives the following relation between upload and
download speed Upload=7.9462+(0.1609× Download)
In order to explore the relation of upload speed with evening time multiple regression
analysis has been done. The result gives following result equation estimate
Upload=8.0378− ( 0.1308 × Evening ) +(0.1596 × Download)
Comparison of the two model reveals that simple linear regression model is the best
estimate to predict variation in upload speed. The best model shows that 36 percent variation
in the upload speed is explained by download speed. Given zero download speed upload
speed is obtained as 7.9462 Mbps. Download speed has a positive impact on upload speed
and upload speed increases by 0.160 Mbps when download speed increases by 1 Mbps.
Regards,
Emma
Appendices

6STATISTICAL ANALYSIS
Answer 1
Statistical technique
Interval estimation of proportion.
Random variables
D: Favorable case (times when speed of download is 40 Mbps or faster)
N: Number of observation
P0: Required proportion
P0 = D/N
Excel result
Interpretation

7STATISTICAL ANALYSIS
The obtained interval estimate can be interpreted as one can be 95% confidence about
the fact that proportion of time with download speed is 40 Mbps or faster vary within the
range between 7.93% and 20.41%.
Answer 2
Statistical technique
Hypothesis test for sample mean.
Random variables
x: sample mean of evening download speed
μ: population mean of evening download speed
n: sample size
Hypotheses
Null hypothesis ( H0 ) : μ ≤ 41
Alternative hypothesis ( H1 ) : μ>41

8STATISTICAL ANALYSIS
Excel result
Interpretation
The p value of the test is 1.0000 which exceeds chosen significance level. The
decision from the test result is non-rejection of null hypothesis. Average download speed in
the evening therefore is not greater than 41 mbps.

9STATISTICAL ANALYSIS
Answer 3
Statistical technique
Test of equality of mean of two independent sample.
Random variables
D1: sample mean download speed for speed test 1
D2: sample mean download speed for speed test 2
μ1: population mean download speed for speed test 1
μ2: population mean download speed for speed test 2
σ 1: standard deviation of download speed for speed test 1
σ 2: standard deviation of download speed for speed test 2
Hypotheses
Null hypothesis ( H0 ) : μ1=μ2( Mean download speed are same)
Alternative hypothesis ( H1 ) : μ1 ≠ μ2 (Mean download speed are not same)

10STATISTICAL ANALYSIS
Excel result
Interpretation
P value from the statistical test result is 1.0000. The p value exceeds chosen
significance level suggesting decision favoring the null hypothesis of no difference in
download speed.

11STATISTICAL ANALYSIS
Answer 4
Chart 1: Scatter plot and fitted regression line between upload and download speed
Variables
The dependent variable for the simple linear regression model is upload speed and the
independent variable of the model is download speed.
Regression output