^{nd}Nov 2022

# MTH220 Statistical Methods And Inference Assignment Sample Singapore

MTH220 Statistical Methods And Inference is a course offered by the Department of Mathematics and Statistics. The course covers a wide range of topics related to statistical methods and inference, including estimation, hypothesis testing, regression analysis, and nonparametric methods.

This course is designed for students who are interested in learning more about statistical methods and their applications. The course will provide students with the ability to understand and use various statistical methods. In addition, students will also learn how to apply these methods to real-world data sets.

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The tasks we’ll cover in this section are:

**Assignment Task 1: Calculate statistical parameters from data.**

There are a variety of statistical parameters that can be calculated from the data. Some of the most common include the mean, median, and mode. The mean is simply the average of all the data points and can be calculated by adding all the values together and dividing by the number of data points.

The median is the middle value and can be found by sorting the data points from smallest to largest and taking the value in the middle. The mode is the most common value and can be found by counting how often each value appears in the data set.

These are just a few of the many statistical parameters that can be calculated from data. By understanding how to calculate these parameters, you can better understand and analyze your data.

**Assignment Task 2: Determine the equation of the least squares linear regression line.**

In statistics, the least squares linear regression line is the line that best fits a set of data points. To find the equation of this line, one needs to calculate the slope and intercept. The slope can be found by taking the sum of the products of the x-values and y-values and then dividing it by the sum of the squares of the x-values.

The intercept can be found by taking the sum of the y-values and multiplying by the slope and then dividing by the number of data points. Once the slope and intercept have been calculated, they can be plugged into the equation y=mx+b, where m is the slope and b is the intercept. This will give the equation of the least squares linear regression line.

**Assignment Task 3: Comment on the results of hypothesis tests.**

A hypothesis test is used to evaluate a claim about a population parameter. The null hypothesis is the claim that is being tested, and the alternative hypothesis is the claim that the null hypothesis is false. The test statistic is used to assess whether the null hypothesis can be rejected.

If the test statistic falls in the critical region, the null hypothesis is rejected and the alternative hypothesis is accepted. Otherwise, the null hypothesis is not rejected. When interpreting the results of a hypothesis test, it is important to remember that a non-rejection does not mean that the null hypothesis is true.

It simply means that there was not enough evidence to reject the null hypothesis. Similarly, a rejection does not necessarily mean that the alternative hypothesis is true. There may be other explanations for the observed data. In short, hypothesis tests provide valuable information about whether a claim can be supported or rejected, but they should not be used to make definitive conclusions about a population parameter.

**Assignment Task 4: Apply suitable hypothesis tests, non-parametric tests, or goodness-of-fit tests.**

Testing is an essential part of any scientific process. It allows us to refine our hypothesis and gather evidence to support or disprove our theory. In statistics, there are a variety of tests that can be used to assess data. The most appropriate test will depend on the type of data being collected and the question being asked.

For example, parametric tests are typically used when data is Normally distributed, while non-parametric tests are more suited for data that is not Normally distributed. Goodness-of-fit tests are used to compare a set of data with a theoretical model, in order to assess how well the model fits the data. Ultimately, choosing the right statistical test is crucial for ensuring accurate results.

**Assignment Task 5: Compute the probability or expected frequency of an event.**

In order to compute the probability or expected frequency of an event, one must first identify all of the possible outcomes. Once the possible outcomes have been identified, one can then calculate the likelihood of each outcome occurring. For example, if a coin is flipped five times, there is a certain probability that it will land on heads a certain number of times.

In this case, the probability of any particular outcome (such as three heads) can be calculated by taking the number of desired outcomes and dividing it by the total number of possible outcomes. The expected frequency is simply the average number of times that an event is expected to occur over a given period of time.

For example, if a coin is flipped five times per minute, then the expected frequency of heads would be two and a half times per minute. By using probability and expected frequency, one can gain a better understanding of how likely an event is to occur.

**Assignment Task 6: Use R to perform data analysis.**

R is a flexible and powerful programming language that is widely used for statistical computing and data analysis. R has a wide range of built-in functions and libraries that can be used to clean, manipulate, and visualize data. In addition, R can be easily extended through the use of user-defined functions and packages.

As a result, R is an excellent tool for performing data analysis. There are many online resources that can help you get started with using R for data analysis. The R project website (https://www.r-project.org/) provides a comprehensive set of resources, including tutorials, documentation, and examples.

In addition, there are many online forums and mailing lists where you can ask questions and get help from other users. Finally, there are a number of commercial software packages that provide an integrated development environment (IDE) for R, which can make working with R much easier.

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