Questions: When in doubt, assume the original claim is "There is linear correlation." Original claim: We will use significance level . 01 . What method can verify our claim? Linear regression t-Test To check the requirements, graph Dotplot Box plot Normal quantile plot Scatter plot Histogram and ensure there are at least 5 successes and 5 failures points are loosely grouped around a line without an obvious curve all outliers are removed there are at least 30 points all outliers are removed that are due to errors points are loosely grouped around a bell-shaped curve Because technology can't check these requirements, we will just move on even though we might stop here and state the requirements are not met for our test. P-value = square round to four decimal places. Thus, we shall Select an answer Conclusion: Select an answer Q evidence to Select an answer Q the claim that the data Select an answer Q.

Solution Steps

The formula to calculate the correlation coefficient \( r \) is given by:

\[ r = \frac{\text{Cov}(X,Y)}{\sigma_X \sigma_Y} \]

Where:

• \( \text{Cov}(X,Y) = 0.24 \)
• \( \sigma_X = 1.0 \)
• \( \sigma_Y = 0.8709 \)

Substituting the values, we find:

\[ r = \frac{0.24}{1.0 \cdot 0.8709} = 0.2756 \]

The means of \( x \) and \( y \) are calculated as follows:

\[ \bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i = 16.0 \]

\[ \bar{y} = \frac{1}{n} \sum_{i=1}^{n} y_i = 15.9533 \]

To find the slope \( \beta \) and intercept \( \alpha \) of the regression line, we first calculate the numerator and denominator for \( \beta \):

Numerator for \( \beta \):

\[ \sum_{i=1}^{n} x_i y_i - n \bar{x} \bar{y} = 766.24 - 3 \cdot 16.0 \cdot 15.9533 = 0.48 \]

Denominator for \( \beta \):

\[ \sum_{i=1}^{n} x_i^2 - n \bar{x}^2 = 770 - 3 \cdot 16.0^2 = 2.0 \]

Now, we can calculate the slope \( \beta \):

\[ \beta = \frac{0.48}{2.0} = 0.24 \]

Next, we calculate the intercept \( \alpha \):

\[ \alpha = \bar{y} - \beta \bar{x} = 15.9533 - 0.24 \cdot 16.0 = 12.1133 \]

The equation of the line of best fit is given by:

\[ y = \alpha + \beta x = 12.1133 + 0.24x \]

Based on the calculated correlation coefficient \( r = 0.2756 \), we conclude that there is weak evidence to support the claim that there is a linear correlation between the variables.

Final Answer