ST2120 Data Science for Business Analytics II Assignment Sample NUI Galway Ireland
ST2120 Data Science for Business Analytics II is the second course in a two-course sequence that provides students with the skills and knowledge necessary to apply data science techniques to business analytics problems. The course covers advanced topics in data mining, including text mining, social network analysis, and time series analysis. In addition, students will learn how to use state-of-the-art machine learning algorithms for predictive modelling and will get experience working with large datasets. By the end of the course, students will be able to analyze complex data sets and make actionable recommendations based on their findings.
This course is offered at the National University of Ireland, Galway (NUIG), and is part of the Data Science for Business Analytics program. This two-year program is designed for students who want to pursue a career in data science or business analytics. The program provides students with the skills and knowledge necessary to work as data scientists or business analysts in a variety of industries.
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In this section, we are describing some assigned tasks. These are:
Assignment Task 1: Define basic terms: experimental unit, quantitative and qualitative variables, population, sample, parameter, statistic, descriptive statistics and inferential statistics, standard error, sampling distribution, and identify these in the application.
An experimental unit is the smallest division of a population that can be assigned to treatment in an experiment. The most common experimental unit is a person, but it could also be a group of people, animals, cells, or objects (e.g., trees).
Quantitative variables are variables that can be measured and expressed as a number. Examples of quantitative variables include height, weight, age, and IQ score. Qualitative variables are variables that can be categorized but not measured numerically. Examples of qualitative variables include gender (male/female), race (African American/Caucasian), and religious preference (Christianity/Islam).
- A population is the entire group of individuals or objects that we want to study.
- A sample is a subset of the population that we use to represent the whole.
- A parameter is a numerical value that describes a population.
- A statistic is a numerical value that describes a sample.
Descriptive statistics are used to summarize and describe data. They do not allow us to make inferences about the population from which the data was collected.
Inferential statistics are used to make predictions or inferences about a population based on data from a sample.
The standard error is the standard deviation of the sampling distribution.
The sampling distribution is the distribution of values taken by a statistic in all possible samples of the same size from the same population.
Assignment Task 2: Calculate the standard error and determine the sampling distribution for a statistic, in common applications, including stating and applying the Central Limit Theorem in the context of the sampling distribution for large and small samples. Discuss and check any assumptions that apply in those cases.
The standard error is a statistic that measures the variability of the sample mean. It is computed as the standard deviation of the sample mean divided by the square root of the sample size.
The sampling distribution is a theoretical distribution that describes all possible samples that could be drawn from a population. It is based on the assumption that the population from which samples are drawn is Normally distributed.
In common applications, including stating and applying the Central Limit Theorem, we assume that the sampling distribution of a statistic is Normal. This assumption allows us to use Normal tables and/or formulas to find probabilities for our statistics.
The Central Limit Theorem states that the sampling distribution of the sample mean will be Normal, even if the population from which the sample is drawn is not Normally distributed, as long as the sample size is large enough.
To use the Central Limit Theorem, we need to check two conditions:
- The population must be 10 times larger than the sample size.
- The population standard deviation must be known.
Assignment Task 3: Construct and interpret a confidence interval for a population parameter, and discuss factors that will result in a more precise interval estimate.
A confidence interval is an estimate of a population parameter that is constructed using a sample from the population. The width of a confidence interval will be determined by the size of the sample, and the level of confidence that you want to have in your interval estimate.
Factors that will result in a more precise interval estimate include a larger sample size, a higher level of confidence, and a more precise sampling method.
Assignment Task 4: carry out a hypothesis test for a population parameter, in doing so, define type I and type II error, the significance level, the test statistic, the power of the test, and the p-value and interpret each of these terms in the application. Complete the hypothesis test by either determining a rejection region for the test statistic, a rejection region for the sample estimate of the parameter, or a p-value. Identify and complete one and two-tailed testing procedures.
A hypothesis test is a statistical procedure used to test whether or not a given hypothesis is true. The null hypothesis is the hypothesis that we are testing against, and the alternative hypothesis is the hypothesis that we believe to be true.
Type I error occurs when the null hypothesis is true, but we reject it anyway. This type of error is often referred to as a “false positive.”
Type II error occurs when the null hypothesis is false, but we fail to reject it. This type of error is often referred to as a “false negative.”
The significance level of a hypothesis test is the probability of making a Type I error. It is typically set at 0.05, which means that there is a 5% chance of making a Type I error.
The test statistic is a statistic that is used to decide whether or not to reject the null hypothesis. It is calculated using the sample data.
The power of a hypothesis test is the probability of correctly rejecting the null hypothesis when it is false. Power is affected by the sample size, the significance level, and the difference between the null and alternative hypotheses.
The p-value is the probability of getting a result at least as extreme as the one that was observed, given that the null hypothesis is true. A small p-value indicates that the null hypothesis is unlikely to be true.
A two-tailed test is a test in which we can reject the null hypothesis if either tail of the distribution is exceeded. A one-tailed test is a test in which we can only reject the null hypothesis if the upper or lower tail of the distribution is exceeded, depending on which direction the alternative hypothesis is in.
Assignment Task 5: Interpret results from inferential techniques in a variety of applications including estimation of a single population mean (large and small samples), a population proportion of successes in a binary variable, population proportions in a multinomial experiment, i.e. the chi-square goodness of fit test, comparing means of two populations (large and small samples, independent samples and paired samples), comparing means of more than two populations using ANOVA, comparing proportions of successes between two populations (large and small samples), inference for model parameters in simple linear regression.
The results of inferential techniques can be used in a variety of applications, including the estimation of a single population mean (large and small samples), a population proportion or the difference between two population means. In addition, these techniques can be used to test hypotheses about one or more population parameters.
When interpreting the results of inferential techniques, it is important to consider the type of sampling method that was used (random or non-random) and the size of the sample. Additionally, it is important to note whether the results are statistically significant. If the results are not statistically significant, this means that there is not enough evidence to conclude that there is a difference between the parameter being estimated and its theoretical value.
Finally, it is also important to consider the practical significance of the results. This refers to whether the difference between the parameter being estimated and its theoretical value is large enough to be meaningful in the real world.
Assignment Task 6: Use statistical computing software to produce output that reports confidence interval estimates and results of hypothesis testing in a variety of applications, and incorporate this output in statistical report writing.
There are a variety of software options for carrying out statistical computing, including R, SAS, and SPSS. Each software package has its strengths and weaknesses, so it’s important to choose one that will fit the specific needs of your project.
When producing output from a statistical analysis, it’s important to include interval estimates (e.g., 95% confidence intervals) and the results of any hypothesis testing that was carried out. This information can help you to understand the implications of your results and to communicate them effectively to others.
It’s also important to make sure that your output is clear and easy to interpret. This means using tables and graphs where appropriate, and labelling all parts of the output so that it can be easily understood.
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