Question 1 – Topic XXXXXXXXXXmarks) The theoretical maximum download speed on a NBN 50 plan is 50 Mbps. Your friend asks you to estimate the proportion of time that they achieve at least 80%, that is,...

Question 1 – Topic 5 (5.5 marks)

The theoretical maximum download speed on a NBN 50 plan is 50 Mbps. Your friend asks you to estimate the proportion of time that they achieve at least 80%, that is, 40 Mbps or more, of this maximum.

To enable you to answer this useSpeed Test 1 Download(4^thcolumn of your data)forall 120observationsand an appropriate statistical inference technique to:

Estimate the population proportion of time that the download speed is at least 40 Mbps.

Hint:Sort data onSpeed Test 1 Downloadto enable you to easily count the number of observations in your sample with a download speed of 40 Mbps or faster.

Question 2 – Topic6 (7.5 marks)

Your friend asks on average does their evening download speed exceed the advertised typical evening download speed of 41 Mbps.

To provide a justified answer to the question usetheeveningdownload speedfromSpeed Test 1 Download(4th column of data),your output from Part A and an appropriate statistical inference techniqueto answer the following question

Is the mean evening download speed greater than 41 Mbps?

Notes:

·The required data for the evening download speeds is in the first rows of your unsorted sample.

·If you have sorted your data onSpeed Test 1 Downloadin Question 1 sort onEvening(3^rdcolumn of data). Alternatively, download your data again.

·Same consideration applies to Question 5.

Question 3 Topic 7 (8 marks)

To check the accuracy of the Speed Test 1 your friend repeated the test using a second speed test, Speed Test 2. On average each speed test should give the same download and upload speed.

Your friend asks you to check if the two tests on average give the same download speed.

To provide a justified answer useSpeed Test 1 Download(4^thcolumn of data)andSpeed Test 2 Download(6^thcolumn of data) forall 120observations in your sample, your output from Part A and an appropriate statistical inference techniqueto answer the following question.

Is there a difference in the average download speed given by the two tests?

Note:
Difference Download Speed(8th column of data) may be used as an alternative toSpeed Test 1 Download(4^thcolumn of data)andSpeed Test 2 Download(6^thcolumn of data).

Questions 4 and 5 Simple and Multiple Linear Regression (17 marks)

Your friend is interested in the relationship between download and upload speed. In particular they ask you to estimate upload speed from download speed.

To do this you develop a simple linear regression model to estimate upload speed from download speed and a multiple linear regression model to estimate upload speed from download speed and whether it is evening or not. Then you choose and interpret the linear model that best fits your data.

Question 4 Simple Linear Regression Model Topic 8

To explore the relationship between download and upload speed useSpeed Test 1 Download(4th column of data)as the independent variable with
Speed Test 1 Upload(5th column of data)as the dependent variable forall 120observationsin your sample and your output from Part A to develop and then explore a simple linear relationship between the two variables by:

·Calculating the least squares regression line, correlation coefficient and coefficient of determination.

·Interpreting the gradient and vertical intercept of the simple linear regression equation.

·Interpreting the coefficient of determination.

Question 5 Multiple Linear Regression Model Topic 9

To explore whether being evening (7 pm to 11 pm) or not also influences upload speed addEvening(3^rdcolumn of data) as a second independent variable, to develop and then explore the relationship between the three variables by:

·Calculating the multiple regression equation and coefficient of determination.

·Interpreting the values of the multiple regression coefficients.

·Interpreting the value of the coefficient of determination. Compare the value with the corresponding value for the simple linear regression model.

Then determine the best model to estimate upload speed by:

·Using appropriate tests to determine which independent variables make a significant contribution to the regression model.

·Then state the simple or multiple regression equation which best fits the data.

Notes:

·You may need to transform or manipulate the given data, before using Excel for the corresponding statistical calculations.

·Use Excel for all statistical calculations. You do not need to repeat any Excel calculations by hand. However, make sure that you define your random variables and include any steps not given by Excel. For example, in a hypothesis test include the null and alternative hypotheses, along with the decision to reject or not reject the null hypothesis.

·Mention any assumptions you need to make, where appropriate justify these from Part A output.

·In Question 4 fit a linear model even if from your scatter plot you decide that a non-linear relationship better fits the data or that no apparent relationship exists. However, mention this in your written answer and/or corresponding appendix.

·Comment on why a test or confidence interval has been chosen. Where appropriate include and refer to Part A output.

·Make sure you interpret confidence intervals and write conclusions to hypothesis tests.Question 1 – Topic 5 (5.5 marks)

The theoretical maximum download speed on a NBN 50 plan is 50 Mbps. Your friend asks you to estimate the proportion of time that they achieve at least 80%, that is, 40 Mbps or more, of this maximum.

To enable you to answer this useSpeed Test 1 Download(4^thcolumn of your data)forall 120observationsand an appropriate statistical inference technique to:

Estimate the population proportion of time that the download speed is at least 40 Mbps.

Hint:Sort data onSpeed Test 1 Downloadto enable you to easily count the number of observations in your sample with a download speed of 40 Mbps or faster.

Question 2 – Topic6 (7.5 marks)

Your friend asks on average does their evening download speed exceed the advertised typical evening download speed of 41 Mbps.

To provide a justified answer to the question usetheeveningdownload speedfromSpeed Test 1 Download(4th column of data),your output from Part A and an appropriate statistical inference techniqueto answer the following question

Is the mean evening download speed greater than 41 Mbps?

Notes:

·The required data for the evening download speeds is in the first rows of your unsorted sample.

·If you have sorted your data onSpeed Test 1 Downloadin Question 1 sort onEvening(3^rdcolumn of data). Alternatively, download your data again.

·Same consideration applies to Question 5.

Question 3 Topic 7 (8 marks)

To check the accuracy of the Speed Test 1 your friend repeated the test using a second speed test, Speed Test 2. On average each speed test should give the same download and upload speed.

Your friend asks you to check if the two tests on average give the same download speed.

To provide a justified answer useSpeed Test 1 Download(4^thcolumn of data)andSpeed Test 2 Download(6^thcolumn of data) forall 120observations in your sample, your output from Part A and an appropriate statistical inference techniqueto answer the following question.

Is there a difference in the average download speed given by the two tests?

Note:
Difference Download Speed(8th column of data) may be used as an alternative toSpeed Test 1 Download(4^thcolumn of data)andSpeed Test 2 Download(6^thcolumn of data).

Questions 4 and 5 Simple and Multiple Linear Regression (17 marks)

Your friend is interested in the relationship between download and upload speed. In particular they ask you to estimate upload speed from download speed.

To do this you develop a simple linear regression model to estimate upload speed from download speed and a multiple linear regression model to estimate upload speed from download speed and whether it is evening or not. Then you choose and interpret the linear model that best fits your data.

Question 4 Simple Linear Regression Model Topic 8

To explore the relationship between download and upload speed useSpeed Test 1 Download(4th column of data)as the independent variable with
Speed Test 1 Upload(5th column of data)as the dependent variable forall 120observationsin your sample and your output from Part A to develop and then explore a simple linear relationship between the two variables by:

·Calculating the least squares regression line, correlation coefficient and coefficient of determination.

·Interpreting the gradient and vertical intercept of the simple linear regression equation.

·Interpreting the coefficient of determination.

Question 5 Multiple Linear Regression Model Topic 9

To explore whether being evening (7 pm to 11 pm) or not also influences upload speed addEvening(3^rdcolumn of data) as a second independent variable, to develop and then explore the relationship between the three variables by:

·Calculating the multiple regression equation and coefficient of determination.

·Interpreting the values of the multiple regression coefficients.

·Interpreting the value of the coefficient of determination. Compare the value with the corresponding value for the simple linear regression model.

Then determine the best model to estimate upload speed by:

·Using appropriate tests to determine which independent variables make a significant contribution to the regression model.

·Then state the simple or multiple regression equation which best fits the data.

Notes:

·You may need to transform or manipulate the given data, before using Excel for the corresponding statistical calculations.

·Use Excel for all statistical calculations. You do not need to repeat any Excel calculations by hand. However, make sure that you define your random variables and include any steps not given by Excel. For example, in a hypothesis test include the null and alternative hypotheses, along with the decision to reject or not reject the null hypothesis.

·Mention any assumptions you need to make, where appropriate justify these from Part A output.

·In Question 4 fit a linear model even if from your scatter plot you decide that a non-linear relationship better fits the data or that no apparent relationship exists. However, mention this in your written answer and/or corresponding appendix.

·Comment on why a test or confidence interval has been chosen. Where appropriate include and refer to Part A output.

·Make sure you interpret confidence intervals and write conclusions to hypothesis tests.