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# Stb 221 Theory Pdf 14

## STB 221 Theory PDF 14

STB 221 is a course that covers the fundamentals of statistics and probability theory. It introduces students to the concepts of descriptive statistics, sampling distributions, estimation, hypothesis testing, correlation, regression, analysis of variance, and nonparametric methods. The course also teaches students how to use statistical software such as R and SPSS to perform data analysis and interpretation.

If you are looking for a PDF download of STB 221 theory, you have come to the right place. In this article, we will provide you with a link to download a free PDF file that contains all the lecture notes and slides of STB 221 theory. This PDF file is a comprehensive guide that covers all the topics and examples discussed in the course. You can use this PDF file as a reference material or a study guide for your exams.

## Stb 221 Theory Pdf 14

This link will take you to a website where you can download the PDF file for free. The file size is about 10 MB and it contains 221 pages. The PDF file is compatible with any device that can open PDF files, such as computers, tablets, smartphones, etc.

In this section, we will show you some examples of how to apply STB 221 theory to real-world data sets. We will use R and SPSS as our statistical software tools, but you can also use other software that you are familiar with. The data sets we will use are available online and you can download them from the links provided below.

## Example 1: Descriptive Statistics and Histograms

In this example, we will use a data set that contains the heights (in inches) of 200 male students at a university. We want to describe the distribution of heights and plot a histogram to visualize it. To do this, we will use the following steps:

• Download the data set from this link and save it as a text file named "heights.txt".

• Open R and set your working directory to the folder where you saved the file.

• Use the command summary(heights) to get some descriptive statistics of the data, such as mean, median, standard deviation, minimum, maximum, and quartiles.

• Use the command hist(heights\$Height, main = "Histogram of Heights", xlab = "Height (inches)", col = "lightblue") to plot a histogram of the heights.

The output of these commands should look something like this:

> summary(heights) Height Min. :60.00 1st Qu.:67.00 Median :69.00 Mean :69.23 3rd Qu.:71.00 Max. :79.00

The histogram shows that the heights are approximately normally distributed with a mean of about 69 inches and a standard deviation of about 3 inches. Most of the heights are between 66 and 72 inches, with some outliers on both ends.

## Example 2: Estimation and Confidence Intervals

In this example, we will use a data set that contains the scores (out of 100) of 50 students on a math test. We want to estimate the mean score of the population and construct a 95% confidence interval for it. To do this, we will use the following steps:

• Download the data set from this link and save it as an Excel file named "scores.xlsx".

• Open SPSS and import the data from the Excel file.

• Go to Analyze -> Descriptive Statistics -> Explore.

• Select Score as the dependent variable and click OK.

• Go to the Statistics tab and check the box for Confidence Intervals for Mean.

• Enter 95 as the confidence level and click Continue.

• Click OK to run the analysis.

The output of these steps should look something like this:

The output shows that the sample mean score is 76.32 and the standard error of the mean is 2.01. The 95% confidence interval for the population mean score is (72.25, 80.39). This means that we are 95% confident that the true mean score of all students on the math test is between 72.25 and 80.39.

## Example 3: Hypothesis Testing and T-tests

In this example, we will use a data set that contains the weights (in kilograms) of 20 male and 20 female students at a university. We want to test whether there is a significant difference between the mean weights of males and females. To do this, we will use the following steps:

• Download the data set from this link and save it as a CSV file named "weights.csv".

• Open R and set your working directory to the folder where you saved the file.

• Read the data into R using the command: weights <- read.csv("weights.csv")

• Use the command t.test(weights\$Weight weights\$Gender, var.equal = TRUE) to perform a two-sample t-test with equal variances.

The output of this command should look something like this:

> t.test(weights\$Weight weights\$Gender, var.equal = TRUE) Two Sample t-test data: weights\$Weight by weights\$Gender t = -5.6129, df = 38, p-value = 1.402e-06 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: -16.05367 -8.44633 sample estimates: mean in group F mean in group M 55.235 69.365

The output shows that the t-statistic is -5.6129 and the p-value is 1.402e-06. Since the p-value is much smaller than 0.05, we reject the null hypothesis that there is no difference between the mean weights of males and females. The 95% confidence interval for the difference in means is (-16.05, -8.45). This means that we are 95% confident that the true difference in mean weights of males and females is between -16.05 and -8.45 kilograms, with males being heavier than females on average.