Two indicators of the level of economic activity in a given...

Name: Problem 39, Chapter 13: Elementary Statistics
Uploaded: 2020-06-28T01:20:35-08:00
Duration: 3 min 30 s
Channel: Jeremiah Mbaria
Description: Two indicators of the level of economic activity in a given geographical area are its median household income and its percent of population in poverty. The table below lists the data for seven states for the year 2008 ; a. Calculate the correlation coefficient between the two variables. b. Test for a significant correlation at the 0.05 level of significance and draw your conclusion.

Two indicators of the level of economic activity in a given geographical area are its median household income and its percent of population in poverty. The table below lists the data for seven states for the year 2008 ; a. Calculate the correlation coefficient between the two variables. b. Test for a significant correlation at the 0.05 level of significance and draw your conclusion.

Two indicators of the level of economic activity in a given geographical area are its median household income and its percent of population in poverty. The table below lists the data for seven states for the year 2008 ;
a. Calculate the correlation coefficient between the two variables.
b. Test for a significant correlation at the 0.05 level of significance and draw your conclusion.

Key Concepts

Correlation Coefficient

The correlation coefficient is a numerical measure that quantifies the strength and direction of the linear relationship between two continuous variables. It usually ranges from -1 to 1, where values near 1 indicate a strong positive linear association, values near -1 indicate a strong negative linear association, and values close to 0 indicate little to no linear relationship. This measure is crucial in economics and other fields to discern patterns between variables such as income and poverty rates.

Hypothesis Testing for Correlation

Hypothesis testing for correlation is a statistical procedure used to determine whether an observed correlation coefficient significantly differs from zero, implying a true relationship exists between the variables in the population. It involves formulating a null hypothesis stating that there is no correlation (rho = 0) and an alternative hypothesis stating that a correlation exists (rho ? 0), calculating a test statistic (often using the t-distribution), and then comparing the resulting p-value to a predetermined significance level.

Level of Significance

The level of significance is the threshold used in hypothesis testing to decide whether to reject the null hypothesis. Typically denoted by alpha (?), a common value is 0.05, indicating a 5% risk of rejecting the null hypothesis when it is actually true. This concept is essential in statistical analyses to control for type I errors, ensuring that any claim of a significant relationship, such as between median income and poverty, is robust and not due to random chance.

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