• Hypothesis testing is a way to use data to make a decision. It helps you figure out whether a hypothesis about some thing is likely true or likely not true.
• In this presentation we will be conducting a hypothesis test to understand how GDP affects life expectancy.

We’ll define the null hypothesis and alternative hypothesis as follows:

\[H_0: \text{No relationship between GDP per capita} \\ \text{and life expectancy.} \]

\[ H_1: \text{There is a relationship between GDP per capita} \\ \text{and life expectancy.} \]

In mathematical terms:

\[ H_0: \beta_1 = 0 \] \[ H_1: \beta_1 \neq 0 \]

\(\beta_1\) is the slope of the regression line from the linear regression that we will conduct.

• We will be looking at a dataset called gapminder. It that contains data on countries all around the globe, including info on Life Expectancy, GDP per capita, Population, Year, and Continent.

1. Re-iterate the Hypotheses:
   • \(H_0\): No significant relationship between life expectancy and GDP per capita exists (\(\beta_1 = 0\)).
   • \(H_1\): Significant relationship between life expectancy and GDP per exists (\(\beta_1 \neq 0\)).
2. Significance Level:
   • We’ll choose \(\alpha = 0.05\).

Perform the Test:

• We will perform a linear regression to examine the relationship between life expectancy and GDP per capita.

Linear Regression Equation

\[ Y = \beta_0 + \beta_1 X + \epsilon \]

R Code for the linear regression

model <- lm(lifeExp ~ gdpPercap, data = gapminder)

• \(\beta_1\) = 7.6488265^{-4}

• p-value = 3.5657242^{-156}

• And because \(\text{p-value} < \alpha = 0.05\), we can reject the null hypothesis \(\beta_1 \neq 0\)

• Therefore there IS a significant relationship between GDP per capita and life expectancy

• In this case, if we multiply \(\beta_1\) by 10,000, that means that according to the linear regression, with every $10k increase in GDP per capita, life expectancy can be expected to increase by ~7.64 years