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 79.1 80.4 55.7 67.5 79.5 37.6 Award Winners 5.4 8.8 3.2 1.7 11.1 0.1 Construct a scatterplot. Choose the correct graph below. B. с. 30 90 30 90 30 90 30 90 Internet Users Internel Users Inlernel Users Internet Users The linear correlation coefficient r is Round to three decimal places as needed.) Determine the null and alternative hypotheses. (Type integers or decimals. Do not round.) The test statistic is Round to two decimal places as needed.) The P-value is Round to three decimal places as needed.) ▼ the significance level, there ▼ sufficient evidence to support the claim that there is a linear correlation between Internet users Because the P-value of the linear correlation coefficient is and scientific สward winners

Answer 1

Scatterplot: Answer A

Scatterplot 10 40 100 20 0 60 80 0 Internet users

Sample size, n =	6
Ʃ x =	399.8
Ʃ y =	30.3
Ʃ xy =	2313.86
Ʃ x² =	28113.72
Ʃ y² =	242.95
x̅ = Ʃx/n =	66.63333333
y̅ = Ʃy/n =	5.05
SSxx = Ʃx² - (Ʃx)²/n =	1473.713333
SSyy = Ʃy² - (Ʃy)²/n =	89.935
SSxy = Ʃxy - (Ʃx)(Ʃy)/n =	294.87

Correlation coefficient, r = SSxy/√(SSxx*SSyy) = 0.810

Null and alternative hypothesis:

Ho: ρ = 0

Ha: ρ ≠ 0

Test statistic :  t = r*√(n-2)/√(1-r²) = 2.76

df = n-2 = 4

p-value = T.DIST.2T(2.76, 4) = 0.051

Because the P-value of the linear correlation coefficient is more than the significance level, There is not sufficient evidence to support the claim that there is a linear correlation between internet users and scientific award winners.