Math Problem Statement

Pictured above are the critical values for the correlation coefficient. Use the given data set to compete parts (a) through (c) below. Use a significance level of 0.05. The data for x values in respective order is : 10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5. The data for y values in respective order is : 9.14, 8.14, 8.74, 8.77, 9.27, 8.11, 6.14, 3.09, 9.13, 7.26, 4.74. A) construct a scatter plot and make the correct graph to match the data. B) find the linear correlation coefficient, r, then determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables, round to three decimal places as needed. Use the linear correlation coefficient found in the previous step to determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables. C) identify the feature of the data that would be missed if part ( B) was completed without constructing the scatter plot.

Solution

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Math Problem Analysis

Mathematical Concepts

Statistics
Correlation
Linear Regression

Formulas

Pearson correlation coefficient: r = \frac{n(\sum xy) - (\sum x)(\sum y)}{\sqrt{[n \sum x^2 - (\sum x)^2][n \sum y^2 - (\sum y)^2]}}

Theorems

Pearson's correlation test
Critical value table lookup

Suitable Grade Level

Undergraduate/Advanced High School