Constructing and interpreting a Hypothesis Test for Correlation using r as the test statistic

Constructing and interpreting a Hypothesis Test for Correlation using r as the test statistic

According to the U.S. Geological Survey (USGS), the probability of a magnitude 6.7 or greater earthquake in the Greater Bay Area is 63%, about 2 out of 3, in the next 30 years. In April 2008, scientists and engineers released a new earthquake forecast for the State of California called the Uniform California Earthquake Rupture Forecast (UCERF).

As a junior analyst at the USGS, you are tasked to determine whether there is sufficient evidence to support the claim of a linear correlation between the magnitudes and depths from the earthquakes. Your deliverables will be a PowerPoint presentation you will create summarizing your findings and an excel document to show your work.

Concepts Being Studied
Correlation and regression
Creating scatterplots
Constructing and interpreting a Hypothesis Test for Correlation using r as the test statistic

You are given a spreadsheet that contains the following information:

Magnitude measured on the Richter scale
Depth in km

What to Submit on your excel spreadsheet:
Introduce your scenario and data set including the variables provided.
Construct a scatterplot of the two variables provided in the spreadsheet. Include a description of what you see in the scatterplot.

Find the value of the linear correlation coefficient r and the critical value of r using α = 0.05. Include an explanation on how you found those values.

Determine whether there is sufficient evidence to support the claim of a linear correlation between the magnitudes and the depths from the earthquakes. Explain.

Find the regression equation. Let the predictor (x) variable be the magnitude. Identify the slope and the y-intercept within your regression equation.

Is the equation a good model? Explain. What would be the best predicted depth of an earthquake with a magnitude of 2.0? Include the correct units.

Conclude by recapping your ideas by summarizing the information presented in context of the scenario.