Supposed you are interested in determining the connection between drunk driving

Question

Supposed you are interested in determining the connection between drunk driving car accidents and severe impact injuries. You hypothesize that victims who are involved in a drunk driving accident who are hit on impact suffer more severe and serious injuries relative to victims who are not hit on impact. You surveyed a group of 32 victims and found that the connection between the two was 0.82. Conduct a statistical test to determine if the correlation between the above two variables obtained from your sample is different from the true correlation in the population. Answer questions below.

a. State the null and research hypotheses
b. Indicate the appropriate statistical test
c. With the significance level set at .05, specify your critical value
d. Describe the direction and magnitude of the obtained correlation
e. Declare your decision (i.e., whether to reject or retain the H0)
f. Explain your decision

Explanation / Answer

Given that,
value of r =0.82
number (n)=32
null, Ho: =0
alternate, H1: !=0
level of significance, = 0.05
from standard normal table, two tailed t /2 =2.042
since our test is two-tailed
reject Ho, if to < -2.042 OR if to > 2.042
we use test statistic (t) = r / sqrt(1-r^2/(n-2))
to=0.82/(sqrt( ( 1-0.82^2 )/(32-2) )
to =7.85
|to | =7.85
critical value
the value of |t | at los 0.05% is 2.042
we got |to| =7.85 & | t | =2.042
make decision
hence value of | to | > | t | and here we reject Ho
ANSWERS
---------------
null, Ho: =0
alternate, H1: !=0
test statistic: 7.85
critical value: -2.042 , 2.042
decision: reject Ho
sample obtained is different from the true correlation in the population

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