Question

A researcher from the University of California, San Diego, collected data on average per capita wine consumption and heart disease death rate in a random sample of $19$ countries for which data were available. The following table displays the data

Is there convincing evidence of a negative linear relationship between wine consumption and heart disease deaths in the population of countries?

Short answer

There is sufficient evidence to support the claim that is a negative linear relationship between wine consumption and heart disease deaths in the population of contries.

Step-by-step solution

Given Information

We need to find whether there is convincing evidence of a negative linear relationship between wine consumption and heart disease deaths in the population of countries or not.

Simplify

Here, using technology, you find the following output:

Consider:

$$\begin{gathered} \mathrm{n}=19 \\ \mathrm{b}=-22.969 \\ {\mathrm{SE}}_{\mathrm{b}}=3.557 \end{gathered}$$

Determine the hypothesis:

$$\begin{gathered} \mathrm{\beta }=0 \\ \mathrm{\beta }<0 \end{gathered}$$

Compute the value of the test statistic:

$\mathrm{t}=\frac{{\mathrm{b}}_1-{\mathrm{\beta }}_1}{{\mathrm{SE}}_{{\mathrm{b}}_1}}=\frac{-22.969-0}{3.557}\approx -6.457$

The P-value is the probability of obtaining the value of the test statistic, or a value more extreme. The P-value is the number (or interval) in the column title of the Student's T table in the appendix containing the -value in the row $\mathrm{df}=\mathrm{n}-2=19-2=17$

$\mathrm{P}<0.0005$

If the P-value is less than or equal to the significance level, then the null hypothesis is rejected:
$\mathrm{P}<0.05\Rightarrow \mathrm{Reject}{\mathrm{H}}_0$