# I need help with using a statistical hypothesis testing process which is used to compare 2 different variables of data

Everything is mentioned in the file. I'm a grade 11 student in the lowest maths class so try not to make it complicated. I absolutely need to get this done and follow the steps from the file and write the essay in that order. Thank you.

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Grade 11 Statistics Assessment Statement of Inquiry “How can using a statistical hypothesis testing process lead us to a better understanding when comparing two different variables of real world data?” ATL Skills Communication Skills: Writing a mathematical report that is well structured and presents mathematical ideas using appropriate tools and formatting. Critical Thinking Skills: Critically analysing data and results to ensure that results are valid as well as analyse for deeper comparisons and limitations of results. Assessment Criteria Criteria C: Communication in Mathematics Criteria D: Real-life Applications in Mathematics Task Your task is to follow the stages of a statistical hypothesis test to determine whether there is a correlation between two different variables of your choice. You will need to: 1. Select the variables that you wish to compare 2. Determine the Null and Alternate Hypothesis that you will be testing 3. Collect the data using a valid sampling method 4. Present the data in an appropriate table and graph 5. Complete relevant calculations to determine the strength and type of correlation and determine whether it is appropriate to find the regression line, and to find the equation of the regression line if appropriate to do so. 6. Conclude and analyse the results from your calculations It is important that you have a well-organised report that shows the development of the hypothesis testing process in a logical manner if you wish to achieve a good score on this assessment task. 1. Selecting the Variables The first thing you will need to decide upon are what variables you will be comparing and collecting data for. You will need to consider the following ideas when selecting your variables and include relevant information in your report: · Will the variables be discrete or continuous data? · Which will be the independent variable () and which will be the dependent variable ()? · Why are you interested in comparing these two variables? · Will you be analysing these variables within separate groups (e.g. Comparing “MEDC and LEDC” or “Male and Female”) To receive a higher score on this assignment, you should be aiming to have two groups to compare to see if there is a stronger correlation for one group compared to another so try to spend a little bit of time to think about what two groups and two variables you are going to use for this report so that you can be more critical in your analysis. 2. writing your hypotheses Once you have determined your variables and groups you need to set up your two hypotheses for testing; the Null Hypothesis, , and the Alternate Hypothesis, . The Null Hypothesis is that there is no correlation between the variables, whilst the Alternate Hypothesis is that there is a correlation between the variables. You should have the same hypotheses for both groups, as you should be comparing the same variables. The process of this statistical hypothesis testing is to determine whether there is enough evidence to suggest a linear correlation between the two variables that you have selected in section 1. After you have written these two hypotheses, you may wish to comment on whether you think the two different groups will have a correlation and, possibly, predict which of the groups may have a stronger correlation. 3. Collecting your data Now you need to collect your data for analysis. You will need to be able to collect sufficient data for both groups you are comparing. It can be shown using Central Limit Theorem[footnoteRef:1] that a sample size of at least 30 for each group should be of sufficient quantity to make a valid comparison. What you will need to research and determine is a suitable sampling method to make sure that the selection you are using is not biased. As a starting point, you may wish to research the following three sampling methods and determine which will be the best for your report: [1: Lesson 5 – Sampling Distributions and Central Limit Theorem https://onlinecourses.science.psu.edu/stat500/book/export/html/25 Date Accessed: 9th April 2017] · Random Sampling · Systematic Sampling · Stratified Sampling 4. Presenting your data Once you have all your data collected you should present this in relevant and clear tables and graphs. When looking at the calculations in the next section, think about how you can set up the table, preferably with a spreadsheet package, to make the calculations simpler. Also, when showing a scatter diagram, you should not include the line of best fit yet as you have not determined whether this is appropriate to do. You should wait until after all your calculations are completed before showing a graph with the line of best fit, if appropriate to do so. 5. Calculating the Strength of Correlation You should now be ready to calculate the strength of correlation. The first step you will need to do is calculate the mean, square mean and standard deviation for each of your variables. For the independent variable, , the calculations are below: For both above equations, the sample size for the variables is . You will also need to then complete the same calculations for the dependent variable, . Once these have been completed for both variables, you will then need to look at the following calculations to find the mean of the variables multiplied and then the covariance of the variables: Finally, once you have your standard deviations for both variables and the covariance you can now calculate the Pearson Product-Moment Correlation Coefficient, , as below: You should then be able to determine the strength of correlation and whether it is a positive or negative correlation, as well as determine whether the null hypothesis can be rejected. For all of the above steps, you should be verifying these calculations with your GDC and showing a screenshot from your calculator where appropriate. If you are able to look at the linear regression line you can use the formulae[footnoteRef:2] below to calculate it: [2: How to calculate a regression line by Deborah J. Rumsey – Dummies http://www.dummies.com/education/math/statistics/how-to-calculate-a-regression-line/ Date Accessed: 9th April 2017] For a regression line in the form we can use the following calculations: Where the results can also be checked and verified by your GDC. All these calculations need to be completed for both groups. 6. Analysis and Conclusion With all your calculations completed and all relevant tables and graphs showing your results, you should now be able to complete your final analysis. It is important that you are making relevant analysis and comments throughout the report, where these can then be summarised in the conclusion and critically analysed. It is important to determine whether there is enough evidence from your study to reject the null hypothesis for either group and to analyse what this means in a real-life context. Think about why there may or may not be a correlation and whether there could be any limitations to the results that you have obtained. Critically analyse the process that you have used throughout the report and state your opinions on whether you think this type of process is a valid analysis of real life data. Are there any further ideas that you could now do instead after this report and what did you learn about statistics and its application to real world analysis. Make sure you also include what you learned out of the process and how you have developed as a mathematician from this assessment. Assessment Criteria Descriptors Criteria C This criterion focuses on the communication of mathematics and so you should make sure that you read the descriptors below and think about how you can make sure that your report meets these various aspects. Make sure you have a clear plan in your introduction that will help you to develop a clear structure to the report. Make sure that you show your data in a clear table ready for analysis, which will be easier if using a spreadsheet package. It is very important that you show all your mathematical calculations clearly and that this is formatted with an equation editor, as well as formatting variables within your written parts correctly with an equation editor. Finally, all graphs and diagrams should be appropriate for the report, with clear titles and labels as appropriate. Level Descriptors 0 None of the descriptors below has been met or there is evidence to suggest academic dishonesty. 1-2 · The report has a no clear structure · Data has either not been shown or is not in a clear table · Mathematical working out has been presented without clear structure · Incorrect or unsuitable graphs have been used 3-4 · The report has a basic structure · Data has been shown in a basic table · Mathematical working out has been structured but not formatted with an equation editor · Scatter Diagrams have been used but are not correctly formatted 5-6 · The report has a good structure that follows the stated plan · Data has been shown in a clear table ready for analysis · Mathematical working out has been structured and formatted with an equation editor mostly throughout the report · Scatter Diagrams are used and have a clear title and labelled axis with an appropriate scale 7-8 · The report has an excellent structure that follows the stated plan and is concise and complete · Data has been shown in a detailed table with relevant information ready for analysis · Mathematical working out has been structured and formatted with an equation editor correctly throughout the report · Scatter Diagrams are used and have a clear title and labelled axis with an appropriate scale and have a correct regression line showing the relevant equation and value where appropriate Criteria D This criterion focuses on real life application of mathematics and so it is important that you think throughout the report how what you are doing relates back to a real-world context. You first need to make sure that you have written correct hypotheses for your variables, which will be linked to correctly identifying the independent and dependent variable that you are testing. Then you will need to make sure that you collect valid data for analysis, both through a sampling method and from a reliable source. This should be clearly communicated in your report and you need to make sure that you have collected a sufficient amount of data also. It is important that you are continually checking throughout the report that results obtained are correct and that your analysis of these results is correct also. Finally, you should make sure that you are performing a meaningful and critical reflection on these results back to the real-life context, which will be easier to demonstrate if you are comparing two different groups of data. Level Descriptors 0 None of the descriptors below has been met or there is evidence to suggest academic dishonesty. 1-2 · No hypotheses have been written · Some data has been collected for analysis · Incorrect calculations have been made and incorrect analysis has been performed · No attempt has been made to relate results back to the real-life context 3-4 · An attempt at writing a Null and Alternate Hypothesis has been made · Sufficient data has been collected for analysis · Calculations are sometimes correct and some analysis is correct based on the results obtained · An attempt has been made to relate the results back to the real-life context 5-6 · A correct Null and Alternate Hypothesis has been written · Sufficient data has been collected for analysis and a valid sampling method has been used or the source of the data is valid and reliable · Calculations are mostly correct and analysis is correct based on the results obtained · Correct meaningful reflection of the results has been made back to the real-life context 7-8 · Correct hypotheses have been written and some initial analysis on the potential outcome has been made · Sufficient data has been collected for analysis, a valid sampling method has been used and the source of the data is valid and reliable · All calculations are correct and the analysis of these results is correct · Correct critical reflection of the results has been made back to the real-life context 2

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