Question

On an international exam, students are asked to respond to a variety of background questions.

For the 41 nations that participated in the exam, the correlation between the percentage of items

answered in the background questionnaire was 0.889. Does this suggest there is a linear relation

between student task persistence and achievement score? Write a sentence that explains what this

result might mean

Answer 1

Given that,
value of r =0.889
number (n)=41
null, Ho: ρ =0
alternate, H1: ρ!=0
level of significance, α = 0.05
from standard normal table, two tailed t α/2 =2.023
since our test is two-tailed
reject Ho, if to < -2.023 OR if to > 2.023
we use test statistic (t) = r / sqrt(1-r^2/(n-2))
to=0.889/(sqrt( ( 1-0.889^2 )/(41-2) )
to =12.124
|to | =12.124
critical value
the value of |t α| at los 0.05% is 2.023
we got |to| =12.124 & | t α | =2.023
make decision
hence value of | to | > | t α| and here we reject Ho
ANSWERS
---------------
null, Ho: ρ =0
alternate, H1: ρ!=0
test statistic: 12.124
critical value: -2.023 , 2.023
decision: reject Ho
we have enough evidence to support the claim that the correlation between the percentage of items
answered in the background questionnaire was 0.889.