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 alphaequals0.01.

Step-by-step explanation:

Hello!

The given information shows the number of internet users per 100 people (X) and the number of scientific award winners per 10 million people (Y)  of different countries.

a)

I've constructed a Scatterplot using the given values of both variables (see second attachment)

The correct option is C

b)

To calculate the correlation coefficient you have to use the following formula:

n= 6; ∑X= 401.2; ∑X²= 28245.94; ∑Y= 29.8; ∑Y²= 231.68; ∑XY= 2268.29

r= 0.80

The parameter of study is the population correlation coefficient ρ (Rho)

The hypotheses to test if there is or isn't a linear correlation between these two variables are:

H₀: ρ=0

H₁: ρ≠0

α:  0.01

The statistic for this test is

This test is two- tailed and so is the p-value, the degrees of freedom of the t-test are n-2= 6-2= 4, so you have to calculate the p-value under a student's t distribution with 4 degrees of freedom:

P(t₄≤-1.89) + P(t₄≥1.89)= P(t₄≤-1.89) + (1 - P(t₄<1.89))= 0.0659 + (1 - 0.9341)= 0.1318

Using the p-value approach the decision rule is:

If p-value ≤ α, reject the null hypothesis.

If p-value > α, do not reject the null hypothesis.

The p-value is greater than the level of significance so the decision is to not reject the null hypothesis. This means that there is not enough evidence to reject the null hypothesis, this means that there is no linear correlation between the two variables.

I hope this helps!

Full text in attachment.

I hope this helps!