My presentation for this homework will be about hypothesis testing. Hypothesis testing is a systematic procedure for deciding whether the results of a research study support a particular theory which applies to a population. Hypothesis testing uses sample data to evaluate a hypothesis about a population.

To perform a hypothesis test in the real world, researchers will obtain a random sample from the population and perform a hypothesis test on the sample data, using a null and alternative hypothesis Clinical Trials Hypothesis tests are often used in clinical trials to determine whether some new treatment, drug, procedure, etc. causes improved outcomes in patients. For example, suppose a doctor believes that a new drug is able to reduce blood pressure in obese patients. To test this, he may measure the blood pressure of 40 patients before and after using the new drug for one month. Advertising Spend Hypothesis tests are often used in business to determine whether or not some new advertising campaign, marketing technique, etc. causes increased sales For example, suppose a company believes that spending more money on digital advertising leads to increased sales. To test this, the company may increase money spent on digital advertising during a two-month period and collect data to see if overall sales have increased.

Scatter plots are a type of data visualization that are used to display individual data points on a two-dimensional graph. They are particularly useful for understanding the relationships between two continuous variables and can provide valuable insights into your data. here is an example of how to use scatter plot to demonstrate relationship between MPG and HP for mtcars.

we do have different graphing we can show relationship. Bar plot is one of the most useful ones.

here is an example of using plotly plot to present data relationship in 3D.

In hypothesis testing, a common null hypothesis for a one-sample T-test is:

\[ H_0: \mu = \mu_0 \]

Where: - \(H_0\) represents the null hypothesis. - \(\mu\) is the population mean. - \(\mu_0\) is the specified value.

Example: - \(H_0:\) The average height of adult males is 175 centimeters.

For a Chi-Squared test of independence, the null hypothesis is:

\[ H_0: \text{There is no association between two categorical variables.} \]

Example: - \(H_0:\) Gender and job satisfaction are independent variables.