Question

& regression test
4 of 15
this test: 24 point(s) possible
this question: 1 point(s) possible
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 = 0.05.
internet users | 79.4 79.7 56.9 67.2 76.8 38.6
award winners | 5.5 9 3.3 1.6 11 0.1
...
determine the null and alternative hypotheses.
h₀: ρ = 0
h₁: ρ ≠ 0
(type integers or decimals. do not round.)
the test statistic is t = 2.54
(round to two decimal places as needed.)
the p - value is.968
(round to three decimal places as needed.)
because the p - value of the linear correlation coefficient is the significance level, there sufficient evidence to support the claim that there is a linear
correlation between internet users and scientific award win
less than or equal to
greater than
time limit: 05:00:00
next

Explanation:

Step1: Compare P - value and α

The significance level \( \alpha = 0.05\) and the P - value is \( 0.968\). Since \( 0.968>0.05\), the P - value is greater than the significance level.

Step2: Determine evidence for correlation

In hypothesis testing for linear correlation, if the P - value is greater than the significance level \( \alpha\), we fail to reject the null hypothesis \( H_0:
ho = 0\). Failing to reject \( H_0\) means there is not sufficient evidence to support the claim of a linear correlation.

Answer:

The P - value of the linear correlation coefficient is greater 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. So the first blank: greater than; the second blank: is not.