Question

listed below are numbers of internet users per 100 people and numbers of scientific award winners per 10 million people for different countries. construct a scatterplot, find the value of the linear correlation coefficient r, and find the p - value of r. determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. use a significance level of α = 0.01.
internet users | 79.9 80.4 57.7 66.4 78.3 38.4
award winners | 5.3 9.1 3.3 1.8 10.5 0.1
construct a scatterplot. choose the correct graph below.
a. b. c. d. (with corresponding scatterplot graphs)
the linear correlation coefficient is r = 0.818.
(round to three decimal places as needed.)
determine the null and alternative hypotheses.
h₀: ρ
h₁: ρ
(type integers or decimals. do not round.)

Explanation:

Step1: Define Hypotheses for Correlation

In testing linear correlation, the null hypothesis \( H_0 \) assumes no linear correlation (population correlation coefficient \(
ho = 0 \)), and the alternative hypothesis \( H_1 \) assumes there is a linear correlation ( \(
ho
eq 0 \) for two - tailed test, which is appropriate here as we are testing for any linear correlation, positive or negative).

Step2: State the Hypotheses

For the null hypothesis \( H_0 \), we state that the population correlation coefficient \(
ho = 0 \) (indicating no linear correlation between the number of Internet users per 100 people and the number of scientific award winners per 10 million people).
For the alternative hypothesis \( H_1 \), we state that \(
ho
eq 0 \) (indicating that there is a linear correlation between the two variables).

Answer:

\( H_0:
ho = 0 \)
\( H_1:
ho
eq 0 \)